Time for a little cross model knowledge
The front brakes on the R3 are the same front brakes on the Daytona 955i. The 955i was notorious as they aged for having spongy and dragging front brakes. It's because of the calipers not sealing well around the piston. Triumph seem to have improved the tolerances for the Rocket, but, on a 10 year old bike like yours, I would not be shocked to find that your caliper seals are going out. If that's the case, they are very easy to rebuild and the kit to do so is very cheap.
I doubt they are dragging abnormally though. HH pads need to be heat cycled a few times as they say to bed in. I usually go on the freeway and heat cycle them by dragging the front brake while maintaining speed in an on/off pattern with time to cool between cycles for an hour or so, let them cool, then go ride them without a second thought, has never failed me yet. HH pads are louder than the organics though, its unavoidable, they have a much higher coefficient of friction, the reason they work so well, and because of that increased friction they stop you better to. Just a small trade off.