Okay, so I've done my homework on restart warping and am ready to give a writeup for those who are interested, and to save anyone else replicating the same work.
Firstly, the basics.
The entire I Wanna Be The Guy game world is split into 9 Sections. Exactly one section is loaded into memory at any given time. Stuff like bullets and enemies can travel between screens within a Section, but when you go through a transition to another Section, everything in the section you were in gets wiped from memory and the Section you're entering gets reset to its starting condition.
The 9 Sections are:
Beginning (contains Mike Tyson)
Megaman (contains KKK and Mother Brain)
Ghouls and Goblins (contains Mecha Birdo)
Center (contains Dracula)
Kirby
Kraidgief (contains Kraidgief)
Minecart (contains Dragon Devil)
Entrance of the Guy
Final Tower of the Guy (contains The Guy)
Locations within each section are described by x and y co-ordinates. In the co-ordinate system used, each screen is 800 across and 600 high. In the IWBTG save editor,
I Wanna Be The Fix, you can modify a save so that The Kid is placed at any co-ordinates, in any Section besides Kraidgief, when you load it. (Kraidgief isn't available in IWBTF because it's intended for fixing legitimate broken saves, but there are no save points in Kraidgief).
The following is a list of all the transitions between Sections:
Beginning to Kirby - dropping down into the Tetris room
Beginning to Megaman - going right from the room with the blue tunnel
Beginning to Ghouls and Goblins - going right from the room with Giant Link
Megaman to Center - going right from the spiky room after the KKK fight
Megaman to Center - the teleport you jump into at the end of the Metroid zone
Ghouls and Goblins to Center - the teleport that happens after you defeat Birdo (the Birdo orb is actually located in the Center Section, not in GnG)
Ghouls and Goblins to Beginning - returning to the Link room from GnG. This is the only two-way Section transition in the game
Kirby to Kraidgief - dropping into the Kraidgief fight. (The whole Kraidgief section is just the scrolling screen you fight Kraidgief on)
Kraidgief to Megaman - the teleport that happens after you grab the Kraidgief orb
Center to Beginning - the two teleporters at the end of Center that say 'Return to Beginning' on them
Center to Minecart - the teleporter to the Minecart area
Minecart to Entrance of the Guy - happens after defeating Dragon Devil
Entrance of the Guy to Final Tower of the Guy - going right from the Incinerator of the Guy
Beginning to Megaman - KKK teleporter in room of Divine Transportation
Beginning to Megaman - Mother Brain teleporter
Beginning to Megaman - Kraidgief teleporter
Beginning to Center - Dracula teleporter
Beginning to Center - Mecha Birdo teleporter
Now that the basic structure of the games areas is covered, let's explain restart warping.
Apparently, in the editor Kayin used to create the sections for IWBTG, he had to put The Kid somewhere in each section. When you press 'r' in a game before making your first save, the game teleports you to the spot in the current section where Kayin left The Kid in the editor. However, for some reason, normally when you go through a transition into a new section, the game first loads the screen that The Kid is on in the editor, and then teleports the kid to another location. In other words, pressing 'r' in most sections will teleport you to somewhere completely different to where you normally start the section.
This is understandable in sections like Center with lots of entrances, but for some reason you even end up at a slightly different location when doing this in areas with a single entrance, like Kraidgief. No idea why.
Here's a list of the places that pressing 'r' takes you to in each Section:
Beginning - takes you to the spot where you start the game
Megaman - takes you to a spot roughly halfway between where you spawn if you enter Megaman from Beginning, and where you spawn if you enter Megaman from Kraidgief
Ghouls and Goblins - puts you where you spawn when entering Ghouls and Goblins
Center - puts you right at the entrance to the room with Dracula in
Kirby - puts you in front of the spike wall that chases you
Kraidgief - puts you halfway further down the screen than where you spawn when you enter Kraidgief
Minecart - puts you at the start of Minecart, where you spawn when you enter
Entrance of the Guy - puts you at the start point for Entrance of the Guy
Final Tower of the Guy - puts you right at the entrance to the final room
However, there's another kind of restart warping besides the type I described above. Remember how I said that the script when going through a Section transition first places you at the location you get to when you press 'r' in that section, and then teleports you to the correct co-ordinates you should be at after going through the transition. Well, with
most Section transitions, if you press 'r' on the same frame that you trigger the transition, you'll stop the game from moving you into the new Section, but the co-ordinate-based teleport will
still happen. In other words, you get teleported to the same co-ordinates in your current Section as you would normally have started the next Section at.
Unfortunately, most of these teleports put you uselessly Out Of Bounds, trap you inside walls, or get you killed. But since I've bothered testing them all, I'm going to list where r-warping while going through each transition puts you.
Beginning to Kirby (Tetris) - kills you on a spike in the same room
Beginning to Megaman - I couldn't get this warp to work*
Beginning to Ghouls and Goblins - puts you above spikes in the room below the Game Over room; you can't escape death
Megaman to Center (KKK) - I couldn't get this warp to work*
Megaman to Center (Metroid) - I couldn't get this warp to work*
Ghouls and Goblins to Center - I couldn't get this warp to work*
Ghouls and Goblins to Beginning - puts you OoB somewhere black; there's no way back inbounds
Kirby to Kraidgief - traps you inside the 'blocks remaining' section of the Tetris room (or an identical copy of the Tetris room, I'm not sure)
Kraidgief to Megaman - traps you inside the wall at the left hand side of Kraidgief
Center to Beginning - traps you inside a wall somewhere
Center to Minecart - puts you above the screen where you fight Dracula
Minecart to Entrance of the Guy - I couldn't get this warp to work*
Entrance of the Guy to Final Tower of the Guy - I couldn't get this warp to work*
KKK teleporter - puts you in the screen of sky directly below Mike Tyson
Mother Brain teleporter - puts in a black void out of bounds somewhere
Kraidgief teleporter - puts you in the Game Over room
Dracula teleporter - gets you stuck in a wall in the room the right of the starting room
Mecha Birdo teleporter - gets you stuck in a wall in the room of Divine Transportation
* I don't know whether the warps I failed to pull off are actually impossible, or whether I screwed them up somehow. Someone may want to investigate further.
Anyway, clearly none of the warps you can do when going through transitions are helpful. The only one that looks even faintly useful is the one with the Dracula teleporter - it allows an alternate route in which you'd beat Tyson, warp back to the starting room, then go to the teleporter and warp into the sky below Tyson. As it happens, though, this is significantly longer than progressing the normal way.
Let's return to the ordinary restart warps though - the ones that happen when you press 'r' at any time OTHER than the frame a Section transition starts. Kurikinton uses two of these: the Kirby one (to skip the Tetris room and the room after that), and the Center one (to warp to Dracula after the Megaman section).
Unused restart warps that scream out as being potentially useful are the one to skip the tower section of final tower of the guy, and a second use of the warp to Dracula in Center, to skip going through the bit of Center that he does after Mecha Birdo. However, neither of these actually helps; to use the Tower warp, which saves 40 seconds, he would need to not make any saves up until that point in the game, which means giving up all his save point abuse - which saves, at a guess, well over a minute. As for fighting Dracula a second time instead of going through Center, it WOULD be faster, except that when you pick up the Dracula orb for a second time, the game doesn't actually teleport you to the fan room. You're just left trapped in the Dracula fight room.
After all this research, there's exactly ONE useful warp I think Kurikinton missed, which is the warp in Megaman. Doing that immediately after entering Megaman from Kraidgief is faster than jumping out of the little tube you start in and saves a few frames, I think. I haven't actually timed it, though.