the check valve is the cheaper and easier fix if it does not fix it then the accumulator could also be leaking down slowly. If it is the accumulator, it should leak out of the vacuum line into the valve cover not good for the oil but you may see it some gas in the line, Anyway just more stuff to check. Again that is if priming the fuel system fixes the problem if priming does not work then you maybe right it is the cold start system.
2005 320 CDI
2006.5 VW Jetta TDI
1991 560SEL (179000 Sold)
1972 280SEL 4.5 ('The Lead Sled' 320000 miles when sold.)
1972 220D (225000 when sold)