Replacing my Floyd Rose floating tremolo...?

I have a nice Zion electric guitar with a floating Floyd Rose tremolo. It's great for some things, but I want to improve my lead playing. It's impossible to rest my right hand on it while picking because it bends the strings sharp. I'd like to replace the whole bridge with a Strat or Tele bridge or similar. Is this possible with the current cutout in the wood? Any advice would be appreciated. Thanks.