May I offer a dissenting voice to all this concentration on glow plugs?
My 200tdi started immediately all last winter without any glow plug use - they're not even wired up. It stands outside, and went a fortnight without being touched at one stage.
I can't see an engine taking 30 seconds to run properly at this time of the year, simply because there's a bit of unburnt fuel slopping around: a couple of firing strokes should clear any such stuff out of the cylinders. A petrol engine, with a manifold full of fuel - yes.
Sounds much more like air getting into the fuel system to me. I'd start by checking the bleed-off lines from the injectors - a tiny split will let just enough air into the top of the filter when it stands overnight to cause your symptoms, but may not leak diesel visibly when the engine is running. Can't picture the filter head on a 300tdi, but if it has a rubber button to prime the system, these can split and let air in. Aren't 300tdi lift pumps a bit notorious for failing, too? They're only about 20-odd quid from Paddock.