There's two ways I can think of making it run smoother.
1. Chainfire3D. It's a root app, found in the market, whose sole purpose is to enable games on devices that wouldn't normally be able to play them. You have to buy it to unlock everything, but I've been able to use the free version on my Moto Droid to play GTAIII better.
2. Delete the audio folder. Once you have everything downloaded, manually delete the audio folder. If the phone isn't constantly trying to play music or SFX, it will run a bit quicker.
The specific apk isn't going to matter, unless rockstar made huge optimizations to code in recent versions, but as you've DLed from the market, that shouldn't matter, no? Overall, I'd recommend against trying to run it. The optimus isn't really made to handle 3D games in general, much less GTAIII. Good luck, though.