Seems like SM doesn't like that GSM is present in memory when it tries to launch the game. Not sure if it has anything to do with the 240p mode that SM normally uses for its UI. Could be possible that there is a conflict between the memory ranges that SM and GSM use that causes SM to break when running alongside GSM. The only suggestion I have would either be to use the original disc in this situation (not optimal if you either prefer to use backups to save wear on your original disc, or if you are modifying the game) or to reburn your backup after patching (as GSM works well with ESR and patched backups, in my limited experience). A modchip would also fix your situation, as it would remove the need for SM, however that's a little overkill for what you need it for (and nowadays, softmodding is every bit, if not more so, capable than a chipped system), so I won't recommend it.
Another option (which may have slower loading times than optical disc depending on the game's disc access pattern) would be to try OPL (either the standalone build along with standalone GSM, or the combined OPLGSM build) and load your game from a USB drive or from a Windows network share. If you had a fat PS2, I'd recommend an internal HDD setup (in fact, if you are willing to spend a little money, I will still recommend such a setup). Network sharing has the potential to be faster when loading than optical disc, if the game seeks a lot when loading then network loading will likely be faster (see: Bully, and likely other Rockstar games).
Regarding MGS with your component cables - I'm not sure about MGS specifically, but if it uses a 240p vmode (as many PS1 games did), then your TV just may not support 240p over component cables (my TV "supports" it, but is a little wonky depending on whether I powered the set up in component mode, or switched from HDMI). Using composite or s-video would likely fix the issues, but as you said (and agree with), component cables in conjunction with GSM is a great way to game.
Chip-free/MC-free homebrew <3
FMCB 1.93 on MC for emergencies, NA
250GB HDD/FHDB 1.93/OPL 0.9.2 (GSM and non-GSM)/PS2 games, NO HDDOSD
80GB HDD/FHDB 1.93/POPStarter rev12/OPL644/GSM0.37/PS1 games, NO HDDOSD
SCPH-75001 (sitting idle, slims suck):
FMCB 1.92 on MC