engine compression won't back feed. With the way the injectors are made, It would take a whole lot of pressure to push the pintle off it's seat. Enough that if you had that much pressure, you'd certainly have other issues like the starter not being able to turn it over and insuffiicient clearance between the crown and the head, among many other things. Basically, not really possible.
Now if they DID have a leak, you'd have fuel getting into the cylinder at the wrong time assuming the pump works. That's usually evident by rattling, clanking, but not like a rod rattle. And smoke. But I aint never seen one "backfeed"-ever. Rare to see an injector "bad" unless it's common rail and I don't think we're talking about common rail stuff here.
You need to know the cranking pressure first of all. Rent a gauge if you can find one. Then post it up. 500 psi is about where you want to see it. 380 is the lowest spec, usually if they're that low they're barely run, if at all. I've gotten them to run down to 350 but not very well, and normally not for very long.
Is there a possibility that moisture could have gotten into the fuel? If so, your pump doesn't like you. They are extremely intolerant of water and air. And gas. If any of those get into the pump, sometimes the plungers will get stuck and then they'll just barely move any fuel, not enough to run usually. Sometimes just one plunger will stick and you will see that when it's removed, one roller will be higher in the pump than the others.
Way I read it, it sure does sound like air. One thing worth noting, these systems don't bleed the same as some do. You never need to "crack" the injector lines loose to bleed the lines. Just loosen the bleeder, crank it over until no more air and/or it starts, and then tighten it up-you're done. Easier than most people make it out to be. On that note, what I have seen way too much of is folks overtightening and/or moving the delivery valves when cranking the injector lines with a 17mm wrench. Once the delivery valve turns in the bore, send the pump back out for repair. All it takes is about a millimeter, hence the reason you always hold the delivery valve with a wrench and loosen the nut on the line while holding the other. I bet I do 5 pumps a year from people who think they're mechanics and they'll go to loosening the lines at the pump instead of the injectors (and neither one needs to be loosened) to bleed the system, delivery valve(s) turn, and the pump is then trashed/needs to be sent out for repair. Sometimes it's cheaper to replace it with a new one.