I have some ideas and tricks for speedrunning this game - on all systems but especially on console. I'm only mentioning things I have not seen discussed/utilized by TS3 players before:

-Out-of-game optimizing-

1. If you go to the Locale settings on your X360 and change the country, you can change the language to Dutch, French, German or Italian. I believe you can also do this on PC. This could be used to potentially save cutscene/dialogue time.
2. The game is available on the Xbox Store, and I assume that installing it on a HDD and turning off Xbox Live would speed up the game, therefore saving valuable time in a speedrun.

-Story Mode speedrun saves- Train Escape:

1. On the section of Train Escape where you have to kill the aliens and wait for Doctor Porkchop to shoot a crate down as a stepping stool, you can actually jump off a box and grab a ledge underneath the crate to climb up early and save time.
2. At the end of Train Escape you can throw a ball from far away to hit Doctor Porkchop's target, making you have to run less far. Andy's House:
3. At the beginning half of the level, move Buzz on top of the red box near Andy's desk. Then have Woody do the same. Have Buzz throw Woody at the desk underneath the phone. Then have Woody climb to the phone. This is the fastest way to beat this part of the level. Junkyard:
4. At the beginning section of the stage you have to avoid the crates that push you into the trash compactor. If you jump continuously then it becomes alot easier to survive this section.

-Toy Box mode-

1. THERE IS A GAME-BREAKING GLITCH IN TOY BOX MODE. You need two players to do this: Have one player hold the camera item. Then have the other player pick up that player. The player that was holding the camera must then press B (the cancel button). When this happens he will suddenly be floating and be able to fly anywhere in the game. If you travel to other sections, they will not be loaded properly and townsfolk/buildings will be gone. This has huge potential for any% and 100% Toy Box mode speedruns. This works on X360 and PS3. (I don't know about the others).
2. You can despawn the buildings in the main section of Woody's Roundup. Go down the well and go to Sid's House. Then enter the wooden hallway that takes you back to the main section. If you look to your right you should see a wooden beam. Jump and climb up it. You can then walk on the out of bounds area to move back to Woody's Roundup without hitting the loading zone. And bam! The buildings are gone.
3. If you are grabbing a ledge when a mission is completed, the victory animation will not execute, potentially saving time.

I have just mentioned what I have found potentially useful to speedrunning here. I do not have a capture card so sadly I can't utilize them to speedrun the game myself at the moment... - but since I've seen no one else mention these I thought I'd describe them. Anyway tell me if you have any thoughts! :)

So I am a 100% toybox runner and i tried the glitches you mentioned above Firstly the game breaking glitch its very useful for any% but from my knowledge not so much 100% During testing however I noticed that you can raise and lower your height using stomping and walk around at the height that you chose after you stomped the ground though if you jump at any point without stomping you will fakll through the floor causing you to respawn at the last area you went to via a well or the default spawning area also to note if you fall in water you will be in an endless drowning loop to pull yourself out of this glitch you simply have to just take damage by any source that causes damage like pixies or TNT The second one I could not manage to trigger like you explained however i found another way to trigger it but might not be a good idea due to how long it takes to pull off How i did it was go to stage coaches entrance then inflate wall jump to get over it walk past stage coach till the stunt park driveway entrance spawns and jump down into that area back track to load the stunt park then head back just outside the tunnel and infinite wall jump out of bounds you should spawn back in the town with the buildings now unloaded The third one I could not manage to get either due to poor timing or game having set values to check for to allow the mission to complete like being on the floor and/or grabbing a ledge for example I do have evidence of attempting these glitches but don't know how to show them here aside from using google drive But this is all just my opinion others may find it more useful than I seem to see it as but yea i tried attempting them and they are all pretty easy to pull off Oh also I did them all on the Xbox one