The K75S has become a little hard to start of late, and also has developed a farting problem on deceleration. I have checked TPS and I can hear a click from it when the throttle is turned. The exhaust joint seems OK also.
What else might be responsible...air intakes possibly?

Easy bits first: Z-tube from the plenum chamber to the crankcase is split; one or more vacuum intake caps missing from the throttle bodies.

Adjusting the TPS helps with the backfiring, belching, and farting when decelerating, but there are additional things to consider.

Are the throttle bodies balanced and around 1 1/2 turns out from lightly bottomed? 

Has the seal at the header to silencer joint turned into fairy dust? 

Are you fully closing the throttle when engine braking? 

The hard starting and an uneven idle could be caused by a cracked Z-tube between crankcase and airbox.  A wonky engine temperature sensor can cause problems like you are experiencing as well.

As per .75 & Dai plus throttle body leaks and incorrect injector spray patterns.
Regards Martin.