Well I have some good news and a caution for the few folks who use this style of nestbox; it turns out it was mostly the type of bedding I was using with this kind of nest box.
Yes, I had a rodent infestation and it wasn't helping the situation at all. But, upon review of the types of injuries and decomp I was seeing, not to mention continued losses even after most of the culprits were dead (I lost about 3-6 AFTER all signs of rat and mouse activity completely subsided). My conclusion was that something else was killing the kits and the rats were just taking advantage/being drawn in by the dead kits.
What explains it though, was mostly my fault. I changed the bedding. Yup, something so simple and dumb cost me almost every last kit. I have been using a thick shredded paper base for years (would shred my junk mail and use it for padding and then offer the moms copious amounts of hay to top off the nests). This became predictably labor intensive the more mother buns I got and it was difficult to compost, plus as complained about earlier - it had a tendency to become papier mache when moistened by urine and was entrapping babies. So this season, I decided to switch to a thick hay base and offer moms more hay for building. Bad idea. Apparently, aside from the fact pure hay by itself does not handle any moisture well, it kicks out of this style of nestbox very easily, and - worst of all - the main reason almost every baby died; it does not CUSHION the babies when the mother rabbit descends into the nest to feed (this kind of nest box is down below the main cage, moms don't crawl in like most kinds of nestboxes, they jump down to the babies and then jump up to the main cage). The only thing that explains the types of injuries I was seeing, is they were being crushed - repeatedly - any time the mother would try to feed them and there was nothing the mother could do to avoid it as there wasn't proper padding.
Unfortunately, I didn't figure it out until I switched the bedding again.
Once I was sure the rodents were still under control, I cleaned everything and re-bred a pair of does (ones that lost all their kits at the very start within a few days of having them). This time I changed to a thick layer of fine pine shavings because it was more absorbent and had a smell that might deter rodents (plus they created a surface that would be easier for me to locate deceased babies immediately for removal, it was very hard to find them in the hay).
This time there has been no early losses like before. The babies are even opening their eyes now and I'm noticing the pine shavings not only held up better than anything else (most of the original nesting hay is gone now, even. I need to give more, but wanted to get these pictures first showing what I'm talking about), it is being compacted down. From the mothers. /smh. They're also still bone dry and very clean.
Conclusion: Type of bedding makes a huge difference in rabbits.
Photographic evidence of this: