I too own a 05 & I know the NOT-START-IN-GEAR-FAULT.
Under the clutch lever pivot point there are 3 wires running into a small thin switch. The holes for these screws are slightly elongated and this allows the centre part to move just enough for the contacts on the clutch safety switch to not contact, thus no starting in gear.
You can loosen the screws off a bit and slide the center bit backwards and forwards to see if you can get the thing to start in gear while pulling in the clutch.
BE CAREFUL THEY SOMETIMES LURCH FORWARD EVEN WITH THE CLUTCH PULLED IN.
If this solves it... Yay...all good. Time for beer.
FOR THE FOLLOWING BE AWARE THAT THE BIKE MAY LURCH FORWARD SO BREIFLY TAP THE STARTER TO CONFIRM THE CIRCUIT IS WORKING ONLY... AND BE READY!!!
ALSO DON'T FORGET THE BIKE WONT START IF THE SIDESTAND IS DOWN WHILE IT IS IN GEAR, SO RIG IT UP SO YOU CAN DO THE FOLOWING WITHOUT THE SIDESTAND BEING DOWN OR ANY LURCHING.
Carefully dismantle the switch and you'll see just how basic a design it is...just make sure you don't drop the contact bush out of the lever.
There are three contact points one long & two short.
If you short across one of the short ones (I forget which) to the long one this should close the circuit and allow the starter to kick while the bike is in gear.
Scrub these contacts with some fine grit paper and reassemble and test.
Don't forget that the center bit may need to be wiggled exactly right for the bits to contact.
That's what I did and it's been fine ever since.
Failing all of this you can permanently short the switch by shorting across the appropriate wires or contacts so it will start in gear but this is disabling a safety so would be considered a dangerous option and YOU DO IT AT YOUR OWN RISK!!!! In fact you follow any advice from me at your own risk.
Good luck. Make sure you post back how you went.
P.S. Bummer about the exhaust. Got no advice for that bit...