The Carb's may need cleaning and or rebuilding. The kits are around $30 per Carb. with around an hour per... labor. I know a guy in Qunicy who is great on them... PM me
I had a very similiar problem reoccurring on my outbourd. I have a 2003 200 HPDI. The problem was a dirty screen in the VST tank. Cleaned it and it ran fine.....Its a common problem on the HPDI's.