Have you tried to use MSI Afterburner to see what it shows clockspeeds wise and potentially raise them there? I'm not sure doing anything with the BIOS is going to resolve this issue as I saw a few posts regarding similar problems and they'd tried BIOS to no avail.
TPU is usually where I'd look for VGA BIOS, but they don't have any verified XFX 6650 XT BIOS:
Extensive repository of graphics card BIOS image files. Our database covers submissions categorized by GPU vendor, type, and board partner variant.
www.techpowerup.com
If AMD's protections are anything like nvidia's then you'd have to jump through hoops to use a different vendor BIOS. Assuming the card is still under warranty flashing the BIOS is going to void that most likely.