57ringo I had a 2001 350 TRX that did the same thing.
When I got my 04 rincon I noticed that it has the same problem.
I don't think that there is much that can be done about it.But I
can tell you what I do,and that is that I have an 18" piece of leather
string that is attached to my keyring, and on the other end is a slip
knot(noose),that I slip over the choke knob while riding.
When I start the bike I pull out the choke, and with slack string I
wrap it two or three times around the thumb throttle. After about
five minutes I take it off and, away I go.
Trailboss