Bugger...what model year is your bike?
Triumph Oz weren't interested in my first rebuild because my bike was 4yrs old....(and the owner of the dealership i bought it from had watched me punt it around our local race track on 2 separate track days - apparently that's not a warrantable activity on an R3
)
I'm not surprised triumph say no, the estimate for my repair was $4,500.00 AUD with nearly $3k being labour as they allow 25hrs for the job.
As for you current issue...dropping in and out of gear could be caused by a bent/worn selector fork or the reasonably common cir-clip problem as well as the worn dogs option.
Good luck!