I went ahead and finished up the recording session last night. It became apparent that I was going to run out of space on my Briefcase, so to make it easier, I've uploaded the entire thing to a zip file. (I left off the Boktai and Conclusion tracks, since they're not necessarily part of the main game - and instead uploaded them to Mediafire.) I'm fairly confident that I've captured all of the relevant in-game BGM specific to MGS4, but I also recorded two choice cutscenes - which I absolutely implore you NOT to listen to until you've finished the game, as they're extremely spoiler-heavy due to its accompanying dialogue. I just had to grab them, though, as they contain some terrific musical cues. In fact, I'd suggest avoiding the entire download period, since there are a couple of in-game track spoilers as well.
Metal Gear Solid 4 Game Recordings Soundtrack:
I've also taken the liberty of re-shuffling the official OST's listing to reflect the unreleased material - as well as placing certain tracks back into the game's exact chronological series of events. So if you're wondering why Drebin 893, Haven Troopers, BB Corps, and Guns of The Patriots are out of order, that's no mistake. Again, this listing contains track spoilers, so take heed.
In addition, you can find another listing where I simply integrated the disc 2 tracks 18-27 alert/caution themes back into the soundtrack's proper order; it never did sit well with me that they chose to place all those at the end of the soundtrack.