I should really build something before i run my mouth too long on theoreticals but..
To me the appeal of a 4n1 bucket lies in building it differently than your typical 4n1 bucket, which I honestly struggle to see the appeal of.
I don't really understand why 4n1 buckets are built the way they are, with the 'backplate' being more or less just a dozer blade with no side angling (whoopee?) and almost all of the utility coming from the lid, and the lid being basically the entire size of the closed bucket. I understand the idea of backdragging with the open lid, and how it can make sort of a poorly-gripping grapple.. But i don't understand why the main other choices the lid gives you is to have 'a normal bucket' and 'no bucket'.
What i envision building is more like a root grapple with a fully closed backwall, where the grapple lid is more like a bucket lid. The way I see it, by the root grapple having a 'shorter bottom' then the full closed bucket, you get more breakout force. Combine this with the fact that you can open the lid to dump from the bottom, and you can space your pins farther apart on the loader mount and get even
more breakout force by sacrificing 'conventional' dump angle. So this would be for breaking hard ground, and could also rake.
Have the space between the 'teeth' taper to a close between the teeth. Then have the lid close
under the teeth and nearly close off the bottom. Loose enough to prevent frequent binding of objects rolling between lid and rake, not loose enough to leak all your material out on a bumpy ride.
Have part of the sidewall of the bucket on the back half, and part on the lid. This would, in my mind, allow you to create a shape between those two pieces that would improve the 'bite' when grappling horizontal objects. The tapering opening between the rake teeth would also create a good bite on vertical objects.
Opening the bucket lid gradually would create variable size openings in bottom of the bucket, allowing for some sifting/screening to be done by rattling loose material in a partially-opened bucket.
Don't crucify me on my MS Paint skills, this is the first time i've tried to create a visual for this idea. But instead of going from 'all bucket' to 'no bucket' and having a 'poorly gripping grapple', i see this as going from 'all bucket' to 'root rake' with 'improved gripping action both horizontally and vertically' and having a bit of rock bucket/skeleton bucket functionality as well. The ability to backdrag with the open lid should still remain.
The geometry of the lid pivot etc would definitely need to be figured out. I just put a circle to give the vague idea that theres a pivot up there, but it's definitely in the wrong place.