A tulip tree that only gets to 20'...? I doubt it.

The tree in the island looks fine. (It is Jap. Maple?) I think you'd be best off to learn how to cope with it. Planting a solid groundcover below would be the best solution ... not a fussy garden in which you're doing ongoing work. In the meanwhile, place a fairly heavy layer of mulch in the island to deal with dropped seeds. If you established a solid planting, that would take care of most dropped seeds and the lawn mower would take care of those in the lawn.

The mushroom form of the small green shrub on a "tree stump" at left end of the island is not good. I'd remove it.

If plants are dying under the Japanese maple, there is something else going on. Of any type of maple, Acer palmatums are perhaps the most compatable with underplanting. They don't have an aggressive, water grabbing root system like larger growing maples.....in fact, you are more likely to damage the maple's very sensitive roots by underplanting than the maple is to discourage or kill what might be planted beneath its canopy.

No deciduous tree is going to be litter-free....and even many conifers/evergreens are quite messy as well. Leaves or needles, seed pods, fruits, cones, even spent flowers will all appear on the ground from time to time in varying quanities and will need to be attended to. btw, maple samaras - what you call helicopters - are pretty harmless and Japanese maples certainly do not produce them in quantities that would smother or kill off other plants!!

I suspect that even in zone 6 there must be some trees that you could plant that remain shorter. I don't think you should be selecting a type when you have no overall plan. If I owned your house I would think about dispensing with the berm and having just a normal sized bed under the existing tree.

I confess that I've never heard of a person hating Japanese Maple. To most it is considered highly desirable. If any of them are small enough to transplant you will have no problem giving them away.