I am TASing the MSX2 version, and am currently researching the game. I found a way to speed up the end of the Green Beret section (the upper left screen in the second pass where the beret goes up to where Dr. Pettrovich is) by alerting him (not at the very start of the screen or he will go the wrong way) and going to the next screen at the same time as him. He will appear on the next screen still running. This can be done at the start , but he will run the wrong way at the end. For a speedrun, a punch is possibly necessary after the alert to ensure that there is enough time to get to the end of the screen before he does. This is the reason for the punch on the following screen.

I am not sure if this is possible on the VC (unfortunately death warping won't work on VC, jaguar_king checked), and I don't know how much time it will save since the VC runs fast and also taking damage here might interfere with Running Man, and the alert will probably count for those running Big Boss Rank, but it is something worth looking into. Here is a video: (out of date)
I am still researching ways to be able to alert earlier and even a way to get the green beret to desync; both would speed the section up quite a bit.

I found a way to save four minutes off the Green Beret jungle section by alerting and desyncing the Green Beret:

This may be able to save time for a speedrun of the Virtual Console version, but I am not able to test that version on emulator. Can someone else please test this since it is a bit difficult to test real time? There are two things here: 1) Moving to the next screen must be done at the same time as Green Beret. 2) The punch in the upper left screen(second punch) must be done right before he changes direction in that corner. That is what causes the Green Beret to desync. The first and last punches are done so that Green Beret does not outrun Solid Snake.

I also found a way to save a couple minutes on the egg by using a deathwarp, and also the deathwarp can be used in quite a few places to save multiple minutes.

I have been busy planning the route, but because drops are on a running timer that does not reset, I am unable to make a test TAS that will reflect what the final will look like. So I decided to start the actual TAS and hope everything works out. I just got done with the Black Color fight, which looks cool.

I found some other miscellaneous stuff as well:
I can make a guard float off the screen.
The game gets confused when doing a double KO at the end.
Speaking of getting confused, how about a game crash?
Here is a glitch in the swamp, but is not useful unfortunately.

I'd be down to test it, but what system has the MSX2 version of MG2? And also, would the Green Beret "skip" work on HD Collection / MGS3 Subsistence version?

By Virtual Console I mean the HD Collection. Jaguar_King was attempting the Green Beret skip on stream, but was unable to get it real time because the timing is tight, and the setup for each attempt takes a while. It would be easier to test on a Playstation emulator to see if the skip is possible on that version.