I just had this same issue on my 2003 660 Touring. I started a thread in this section...for me, it was the TSS (Throttle Safety Switch -- search this term and you'll find a couple sticky's on this topic). Engine would start fine, idle, then after driving just a short time, it would cut out...have to pump the throttle to 'catch it' then re-fire and keep going.
I took the throttle assembley on the handle bar apart, then removed the single screw holding the switch in place (for the TSS and Kill), then once the switch was out, I took the switch itself apart and removed the bronze contact for the TSS. Put it all back together (careful -- couple little springs in there!), fired up the sled and problem solved. Kill switch still works as normal.
I don't advocate this as a long term solution (I have the full part on order) but it did solve the issue. I put on about 30 miles the other night with zero hesitation issues.
I looked at all the things you are looking at chasing this issue; it was none of those...
Hope this helps.