Put a barrier--perhaps a double row of edging-- between the other parts of your yard and this dead zone and plant lamium. The reason for the edging barrier is that lamium is invasive but it grows very well in poor soil and shade and will fill in that area very well. You can walk on it and rake up the debris in fall and it comes back in the spring. It is practically indestructable. The only downfall is that it spreads to areas you don't want it if you don't contain it.

A second option is to plant an everbearing shrub in front of the dead zone to hide it. Then just leave that area as is

If cutting down the tree were an option, i think the range of plants you could use would open up. What about a few raised beds with a path and bench? It would be some work to establish the beds and path but then you could plant with hostas and forget about it. I think you could deal with the tree mess by mulching the beds each fall with leaves, the idea being the mess from the tree would add to the mulch. I think the hostas would benefit from a thick mulch in the winter as well. This would cut down tree clean up to just the path and bench areas. I think once all this was established it would be fairly low maintenance.
I have made a flower bed this year that is shaded by my house for most of the day but gets direct sun in the late afternoon. I would love to fill this bed up with hostas, lily of the valley, astilbe and other shady perenials but im just not sure if the shade from the house is too deep or not. Any experience with other shady spots?

Mari--
Your shady spot sounds just like the front flower bed against my house which faces north. I have hostas and ferns and have had lily of the valley which I pulled out because it was too invasive. I'm sure most shade perennials would do well in your yard. Just make sure they are true shade perennials and not part shade I grow impatiens and begonias which love it there too.