Sebastian wrote
apart from the fact i don't know if it'll work on the tilted/carved body and neck.
Your problem is going to be bridge height. The TOM is designed higher than the Strat bridge, to cope with the neck angle. The carving between fretboard and bridge is rather flat. If you are okay with having a tremolo 'ring' made just like the humbucker rings on your Les Paul, you could get away with it.
The one tremolo that might suit your needs I'd say is the Hipshot Tremolo. It is full floating, good quality and rests on the ubiquitous two stud screws. It does need routing in the guitar and you would need a ring as mentioned, but it's not going to look out of place and sustain a lot better than a Floyd.