Oh, I've thought this is the TAS already.
Well, a TAS would be wildly different than this. The fastest way to increase your movement speed is air strafing rapidly. I couldn't calculate the "golden ratio" between number of air strafes and the degree change depending on actual movement speed, but solely this trick would save a lot of time.
An easy way to understand this is that the maximum speed Gordon can go is probably ~
edit4: much more than2000units/speed, while the "running" speed is around ~400unit/speed (don't trust me, I played HL ages ago).
The TAS would aim to pass each door with that maximum speed. Also when "hitting a door", a (standup) countjump should be used for fastest speed recovery (ducking for 1 frame, making a 180 degree turn with correct turning speed and jumping once touching the land). Oh and I don't even mention FPS_MAX trickeries.
btw,
http://www.youtube.com/watch?v=VtI5HM7GVGY#t=48 -> hitting the wall or it's just the map transition?
around ~4:30, in theory, wallsliding gives a very slight boost while strafing there, but it's very hard to pull it off in real time and probably a TAS could make better strafes than falling on wall.
I know it's a TAS once someone able to pull objects while boosting off it infinitely, same way as in ~4:44.
At ~7:48, a wall bug would be better (90 degree facing towrads a wall, forward and duck). Next scene why not jump on scientist and barney head?
Also I would watch a multiplayer speedrun, where players boosts through walls in narrow areas, so one player can advance scripts/entities/transitions while the other one can go to the next part, but people should argue about playing single player with multiple players.
edit: tripmine can't be used to boost through walls? probably an NPC who can jump is required to do that like Barney.
edit2: or snarks?
edit3: "jumpbugs: 14"? I admin I didn't watched it fully, but was there actually a jumpbug (jumping down to a platform while ducking,release duck and jump when 2~4 units above the floor)? I saw mostly edgebugs (falling no a slope wall to avoid taking damage and saving horizontal speed) and "slow wallbugs" (jumping between 2 walls closing in 45 degree)
edit4:
http://wiki.sourceruns.org/wiki doesn't contains wallbug which would save time (I wrote it for 7:48 in this post).
http://wiki.sourceruns.org/wiki/Sharking depends on sv_airaccelerate and another variable (sv_airmove?), so it's different between games
http://wiki.sourceruns.org/wiki/Object_Boosting totally right, the game reduces velocity if it reaches more than 4000, so if you maintain it 3999.999, you can stay on that value.
2-2 2nd screen RWJ is improvable with 1 frame, but gives a much worse knife thrower (hitting himself). Tried some delays, nothing good. And everytime I tried to save somehow a frame on 2-2 last (3rd) screen, I was always much frames behind.
Currently getting a wrong knife thrower at 3-1 2nd one. Trying to sacrifice as few frames as possible. edit: Currently I need to sacrifice 
(he should stop at midway and think about his life for a few seconds)
And also removing half pixel at the end of 1-1 doesn't change boss 1. So I'm out of ideas to improve the pacifist 1-1 and boss (I don't see the possibility either).
edit: also I'm curious why specific "sticky floors" can be avoided why some of them always "sticks"?
For example, first one avoidable, second one isn't (in the pacifist one)
So, here's the NewPPU "normal" credits movie.
To recreate your result (not the above mentioned), I had to remove "R" on 2144th frame.
I've uploaded a movie I think it should sync on console: http://tasvideos.org/userfiles/info/13598421770779436