In each level, each piece has 32 different locations it can appear at, sometimes minus a few that were evidently removed during development and never replaced. A few enemies are also designated as potential piece holders; these pieces are added to the rotation for both #1 and #2.
In addition, there's a "lockout" restriction on placements, which I haven't fully decoded yet. After placing piece 1, the game makes sure not to place 2 in any location sufficiently close to 1, and likewise doesn't place 3 close to the 2 (no idea how it determines "sufficiently close," but that's definitely the type of system it uses, so I doubt there's a way to squeeze all three Wild Canyon pieces into the bottom floor while complying with the lockouts.)
If you get one or more pieces and then die, the stage remembers the locations of the pieces you got, and rerolls only the unobtained ones in accordance with lockouts; still, if you're doing a speedrun segmented by death, the lockout is trivially circumvented by obtaining the pieces in reverse order. You still have to keep trying until the piece spawns in your location of choice, but at least it's possible this way; even if you can get the generator to throw you all three of the best locations on consecutive lives, from a realtime perspective this is probably slower than a good 1-life layout (except in Death Chamber), not to mention it doesn't show nearly as much of the stage to the watcher.
A list of hints enumerating every piece in the Dreamcast version can be found at http://soniccenter.org/sm/files/sa2huntwcrip.txt
and so on, changing "wc" to each of the other stage initials. There's at least one piece, and probably many more, that were removed between SA2 and SA2B, and maybe some that were added in that time but I can't think of any possible examples of the latter, at least not in single-player mode. If I ever get a hold of the SA2B hint lists and they turn out to be different, I'll provide those too.
Current speedrun routes for hard mode are as follows:
Wild Canyon 3-1-2
Pumpkin Hill each piece on a separate life, so might as well go 1-2-3 to take advantage of radar. The fastest game time also requires an annoyingly long setup where you have to die, after gliding all the way to the edge of the level, twice. From a realtime perspective I don't even want to think about how ugly this level would be.
Aquatic Mine 3-2, die, 1 (or I guess in a TAS, there's no downside to getting 1 first, dying and getting 3-2.) 1 and 2 are located in opposite extremities of the level, so anything that gets both in a single life is going to appear tedious, especially on GC. Fortunately, both 1 and 2 are right next to spikeballs where you can die with a minimal waste of real time.
Death Chamber 1-3-2
Meteor Herd 1-3-2
Dry Lagoon - the fastest route goes 2-1-3 but may only be possible on Dreamcast. By my understanding of Screw Kick physics and how they changed between versions, 2-1-3 should be the same
Egg Quarters 2-3-die-1 (actually 2-die-3, 1, because you can squeeze out a slight bit of time by dying as part of the setup that gets you access to key 3). Attempting to visit 1 and 2 in the same life is probably a hopeless loss of time, but depending on how well it's possible for a TAS to conserve height over a long glide
, you might be able to nip 1, stay on the wrong side of the wall, then cut straight across the level, hopefully emerging in the Snake Altar so that you can get 2.
Security Hall each emerald on a separate life (in a non-TAS, I find the 3-1-2 order most convenient), and the deaths are practically immediate. You really don't want to TAS the SA2B version of this level unless you can find a somewhat fast way to sneak into "that" safe while it's locked. It would just look too poor otherwise.
Mad Space 3-1-2. Going 3-1-die-2 may potentially be about half a second faster, but definitely not worth it in realtime or in aesthetics.
I leave you with a prop bet: When those guys finally get around to Cannon's Core, will their first TAS of the level be...over/under 66.0? [EDIT:] Over, by a huge margin.