All I can say after listening to that is WOWOW
Poor turbo diesel (and starter) !!
If this were a normal 1.6TD I'd say you have timing WAY off or some dead cylinders...
Since you have both a franken engine
and a franken pump, not sure what advice to give, you're in very experimental territory and kind of on your own here.
About the only thing absolute you can rule out are compression numbers, do you know the compression numbers?
I mean you literally have an engine and pump that is a mish-mash of parts unlike anyone else's in the world, so collaboratively diagnosing things over the internet becomes damn near impossible in my mind.
We all know the 3 things diesels need to run, and the fact that it eventually starts and idles proves it is at least getting those 3.
Beyond those 3 things there are a million things that take over to make it go up and down the road optimally and efficiently.
I think this is one of the well known issues with the AAZ head on a 1.6 is poor cold starts. You have definitely proven that with the sound clip.
I'm afraid it's just the nature of the beast you have created...
I would completely rule out compression and air leaks in the fuel then just get to tinkering/experimenting with slightly different static timing values next. Just change one thing at a time and test.
You are in uncharted territory, no one out there is going to be able to tell you, "oh yea just set this thing to x.xxmm and turn this screw here and this one here and you should be good", it is all up to you.