how about two or three baskets one on top of the other? As soon as it goes through one, it may have slowed down enough to not go through the other?
Also, for the physics of it, force is change of
momentum over time (impulse). In this case, you want the lowest force possible on the egg and newspaper, so you want the egg to change its speed as slow as possible (momentum is mass times velocity). How about folding it accordion-like as many times as possible somehow? (and of course, leaving enough space in between each fold to give the egg time to fold the newspaper and not just crash through it)
I think some kind of shape like that would be optimal. Now for the part where they're dropped one after the other, I guess you'll need some kind of ramp to allow the eggs to get out of the way before the next one comes in, and quick enough, although that sounds annoying to have to do.
But yeah, that's the physics of it usually. An interesting case is in cars. The hoods for example, are made to crumple easily upon impact because in a crash, the act of crumpling gives the car more time to change its momentum and thus receive a weaker force to itself (and the driver). I don't know if you knew that, but I think it's interesting anyway. Good luck,
ordirules