For what it's worth , we have a JD 6620 , used in summer as a roadside ditch cutter tractor ,in winter as a snow removal unit . It developed a peculiar activity similar to yours ,with a little begging and pleading , they let me look at the JD website , while I was at the dealer's ,it turns out , I didn't know that there is a tiny little screen , inside the inlet for the fuel injector pump , it had become clogged over the winter run with an assorted mess of who knows what . If you go to remove it to clean it , be advised ,some of them have a spring loaded check ball ,just underneath the inlet screen fitting -ask me how I know - Anyway ,look on the side of the injector pump ,as well ,down near the bottom of the pump body , there should be another drain for the pump ,do not open it while it is under pressure , you're in for a nasty surprise ,if there is water there as well ,advise the tractor owner to be prepared for a pump replacement - they are not cheap , by the way -Good luck , good hunting -

Roger Rutledge
Technician/Shop Foreman
Green Park Services
Brantford, Ontario, Canada