There are a few XG MIDI's for FF8, but they usually aren't as good as the GM ones (even using the Yamaha Synth.)
You may notice that some of the SGTs appear to have the same name. (such as battle2-s.sgt and battle2-xg.sgt. There are numbers at the beginning of the names, but I'm not what they are and I can't check right now.)
The ones ending in 'xg' are the XG MIDIs.
BTW: You can also use Dag's FF8 Configurator to listen to the SGTs, if you have it.
About the FF7 MIDIs, I'm not sure I follow what you mean by losing the instruments when you extract the MIDI's. They always work fine for me.
Just make sure if you use the AWE MIDIs that FF7.sf2 is loaded into Bank 1, NOT the Synth Bank.
The General MIDIs, in all their mediocre glory, will work with pretty much any synthesizer (even crappy FM Synthesizers *shudders*).
The Yamaha MIDIs work with pretty much any Synth, but they'll sound like crap and you'll get some really freaky effects (i.e. A synth bass playing in place of the reverse symbol in the Opening Mission music.), unless you use a Yamaha XG Synthesizer.