it would seem a inj pump problem, air in the system would seem the most likely cause, is it possible you missing it?not seeing it? thats an easy case, air gets in, esp after a few minutes of sitting. usually an easy one, its usually the main seal, 1st that is. other seals may have problems as well. takes a while of cranking for the inj pump to get primed, again, and fuel (enough) to get to injectors. its also very possible an internal problem. <perhaps it takes a while for pump to build pressure up, and/or get on the intake,low pressure side, fuel to flow. then it never has free fuel flow, or enough pressure. id do a simple test. unhook inj lines @injectors. dont just crack. another thing you can do/i would do, relieve cyl pressure. either take out glow plugs, or injectors. in this, with inj lines off of injectors, you will crank, or if you take my advice, let engine turn freely, freewheel. let sit like you normally have problem. so maybe at least 1/2 hr sitting. you want to see whats coming out of that side on inj lines. crank freely for a while, if you think starter will, or could be a problem, feel for too much heat. theres really no pressure there, just turn it over and see whats coming out of your lines.
if you have glow plugs out, do not hook up inj lines to injectors!