If you want to go crazy with a FR, try the Ibanez S series. The ZR trem is really stable & can take abuse very well. Tested and proven. It's made out of a thin piece of mahogany so the bass is not the LP-ish kind of "deep" sounding.
For fixed bridge Ibanez guitars, you have many options to choose from.
I don't think think the RG fixed bridge guitars are suitable since your only option is the RG321 and RGT6EXFX. Both made of Mahogany, a tad bit dark sounding. might not be suitable.
Consider the RGA series. Mahogany with Maple top and fixed bridge. Basically your current guitar with a fixed bridge instead.
I would not recommend the RG tremolos with the Edge III bridge. Stable yes but when you need spare parts, you are in trouble.
phew, I hope that helped. If you are wondering why all the guitars I recommended are Ibanez, I can only say that they are the one of the most versatile guitars around
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