well, the TRS-505, or any single locking trem, wouldn't stay in tune as well as a double lokcing trem (your standard OFR varient).
The FR's stability comes from the fact you have a lenght of string, that is locked (isolated) so only that lenght is affected by the trem. Nothing will (and should) shift/move, hence the incredible stability of a good floyd rose.
The TRS-505, is just single locking, so you have movement on one end of the strings.
Any movement in a locking system is a compromise on stability.
Thats why the Ibanez FX-Edge bridge (a fixed bridge, double locking system) is crazy ass stable and a Floyd Rose just drops short (since it moves) and then you get your single locking stuff lah etc etc.
Get a Gotoh. its about USD125 overseas, and should retrofit most licensed fr routes. You can find diagrams of the Gotoh licensed FR online with measurements.