Of all the jobs in boats ...including messing with heads and holding tanks ...priming the engines is my least favorite. There is no way around it but patience. And, although I've never run the tanks dry, that case takes way more patience than others, because the whole loop gets filled with air, putting a very large volume of air into the system, which ultimately needs to be pushed all the way out to the return. And, that's a lot of pumps on the lifter pump or a long wait with a primer pump -- and a lot of splatter to soak up along the way.
When one only lets a little air in, for example, when swapping a filter and then filling the new one up as much as possible, or fixing a fitting, the engines can often just push most of it out in a few cranks and get going to clear the rest.
But, when more air gets introduced, such as when swapping injectors, everything downstream from that point can have air in it. Sometimes I've been able to go right to a nearby "relative high point" and bleed it there, e.g. the next injector or highest injector. But, the least frustrating sequence seems to be to work it in order...start getting just ahead of where I introduced the air filled filled with fuel, and then work up from there.
In some cases, such as when I replaced some fuel lines, and let a bunch of air in, I was able to bleed it as the "next" major point, in that case, the primary fuel filter or the pump's bleed screw, without having to bleed all injectors. In other similar cases, I was less patient about bleeding the pump -- and pushed the air down the line to injectors and pump and had to bleed a bunch of different places.
My mechanic had more refined judgement than me. He'd know based upon the repair if he could "short cut" the process give it a few cranks, bleed in just one place local or a bit downstream from the repair, or bleed it systematically, step by step, until getting to the "next point" and maybe the "next next point" and finding free flowing fuel at both.
But, what I basically learned is that it is best to bleed more early on than later on. Turning over the engine moves air downstream. If it moves the last bit of air off to the return line -- great. But, if it moves it from a situation where one bleed point could get rid of it, and now it needs to be bled at multiple places -- not so good.
In the case of running a tank dry, I'd have bled at the input of filter until good (often times this can gravity feed). Then the other side of the filter, then the compressor pump, then the lowest injector, then the next one, and just worked up. That way, I wouldn't be cranking the engines a lot, or get frustrated. At least when I got to the end of the sequence, I'd *know* they'd start.
My engines are perkins. Yours might be Lehmans (while guessing). Each engine has a slightly different bleed sequence. It is in the owner's or workshop manual. If you don't have one for yours, yet, I'd grab one from the Internet. If a fuel gets dirty underway, you'll be in the same position of needing to bleed to to the swap. So, with everything else going on while underway, you want to be able to do it systematically and with confidence, even if it takes longer. I think, at the least.
The upshot is that the more air gets into the system, and the farther along the way that it makes its way into the system, the less likely you are to be able to "push it through" and the more likely it is that you'll save time and frustration and (and possibly making it worse before making it better) by doing it systematically.
As for why a couple of hours can make a difference. It could have been that the next attempt was the lucky one. It could also have been that some of the suction moved the air through. If your batteries got low from trying to start and got charged by the other alternator or genset, that might have remedied a 2ndary problem.
More than likely (in my estimation), the bouncing around underway caused the pockets of air to get shaken loose and move upward, where came together farther along the loop and were more easily expelled when starting. At least that's my guess.