If it starts instantly, then I don't think it is the glow plugs.
If it starts instantly, then it is probably not an injector leaking return fuel.

You are losing pressure in the rail.
It could be the pressure is being released from the rail via the pressure relief valve. This valve is normally "open" so it closes when powered.
It could be fuel starvation to the high pressure pump. With a new filter, and the fact that it runs fine once going, I might suspect air in the fuel line after sitting for a long time.

If you turn the key to the "run" position, but do not start it, the electric lift pump will be running. If there is air in the lines, you should be able to hear it rushing though the lines and purging back to the tank via the high pressure pump's return fuel line.

__________________
Greg
2012 S350 BlueTEC 4Matic
2007 ML 320 CDI
2007 Leisure Travel Serenity
2006 Sprinter 432k
2005 E320 CDI
1998 SLK230 (teal)
1998 SLK230 (silver)
1996 E300D 99k, 30k on WVO
Previous:
1983 240D, on WVO
1982 300D, on WVO
1983 300CD, on WVO
1986 300SDL 237k, 25k on WVO (Deerslayer)
1991 350SDL 249k, 56k on WVO - Retired to a car spa in Phoenix
1983 380 SEC w/603 diesel, 8k on WVO
1996 E300D 351k, 177k on WVO