Joe,
I "live" in Glenwood Landing (Sea Cliff/Glen Cove area), but prefer to be at my garage in Southampton
but the kids always have something on the weekends with school, band, etc. nowadays so...
Fuel pump should be a relatively easy repair/replacement, but could be messy. Any shop should be able to do it if you positively know that's what it is. Just don't listen to "other" diagnosis.
My good friend and fellow Cobra enthusiast Joe Manning has a shop here in Sea Cliff (specializes in vintage cars) and can help too.