+1 on turning the distortion on the amp DOWN. It will sound thin if you use too much.
The other way to go, which is the BEST way to go, is use the power tube distortion, not the preamp distortion. This is the sweet sounding part of any tube amp. You have to crank the shit out of the gain on the clean channel, and it'll be loud (unless you use a brake) so back your mic up or make sure it's spl rating is high enough, but when power tubes break up, it sounds killer!!!
Also, mic'ing 2 different cabs/amps at once helps alot. If you can't track em both at the same time or only have one amp, do overdubs but voice the amps differently than the first track. Then mix the two, and you'll get a better image that way. Or, if the guitar player insists you don't mess with his tone, track one in the Left speaker and one in the Right. Instant big guitars.
+1 on ditching the strat for anything but a clean sound. Get something with humbuckers. Gibson PAF's, Burstbucker, 490's, Seymour Duncan '58, or PRS makes excellent sounding pickups. Anything but EMG's!!!! <- those sound like a blanket is over them.
At the very least, get a mini humbucker for your strat in the bridge position.
