Fiend

I recently bought an Audi A3 2006 2.0 TDI 170hp DSG. It's generally great but has a persistent problem with a slow / rough start from cold, usually taking a few seconds for the engine to kick in if it's been left overnight / all day. If the engine has been on recently it will start fine:

https://vimeo.com/144744431

The slowness / roughness of the start is in proportion to how long it's been left, although over 12 hours it's pretty much similar. If I start it like this (i.e. badly), turn the ignition off and on again, it starts a lot quicker.

The temperature has no effect whatsoever (5'C start the same as a 20'C start). How recently it's been running has the only effect.

There seems to be no effect from using the battery beforehand (e.g. listening to stereo, turning ignition on and off without starting).

There are no other running / stalling / juddering problems once the engine is running. It never fails to start.

...

I've taken it back to the dealer and had the following work done under warranty:

Fuel pump changed (there was evidence of contamination and oil seeping in, I've run through some super diesel with a fuel cleaner since then).
Fuel filter changed twice (before and after fuel pump change).
Glow plugs replaced.
New battery.
Dual mass flywheel replaced (local Audi specialist A4Audi and dealer suspected it could be this - blame them if it seems a ridiculous idea, not me!).
Also done normally: New cambelt (as part of standard 80,000 mile change).
Also the dealer checked with Audi and apparently the fuel injectors were replaced in 2013 under a general recall.

...but the issue still remains. I have it booked in to have a proper VAG-COM diagnostic (the dealer is a small general dealer and doesn't have vag-com), but any ideas in advance would be helpful.

Fiend

Update: The mechanic had a look at it today, there were no error codes coming through on VAG-COM, and he was pretty sure it was the tandem fuel pump that was loosing pressure slowly when the car was sitting (pretty sure the dealer only replaced the other fuel pump (the one before the fuel filter?)). He's kept it in for more testing though.

Does that sound feasible??