I've been looking at the Gates Carbon Drive and was interested to know if it would it be possible to put a Gates Carbon drive system on a Trek FX-S5 ? I'm planning to use the bike mainly for commuting to work. So want to avoid the Oil/Grease/Chain mess without getting into a Lycra suit.
But if you're dead-keen to do this there may be a way to get a proper frame-builder to cut the stay and fit some sort of a "gate" or structural member that can be opened, then closed to restore rigidity. Something vaguely like the threadded latch on a climbing carabiner?
You'd also swap out both rear dropouts with horizontal ones for tensioning the belt.
Expect this work to cost a lot of money, and there will be repaint costs too.
If you have an aluminium frame this will basically be impossible. With steel it should be cheapest, and carbon fibre I don't really know.... Do talk to a qualified and expert framebuilder, don't try and do it yourself.
Your final option is sell off this bike and buy one with the specs you really want. A racey bike like your trek, with a carbon belt and an IGH or singlespeed is relatively uncommon.