Hello, my name is ***** ***** I will offer suggestions that might help.
First, as you have found out, LED remodel recessed ceiling fixtures usually come in micro sizes and 4, 5, and 6 inch sizes.
I offer several fixes, the preferred is last.
About the only way that you can use these smaller ones would be to use what is called a"goof ring" which would probably be a last resort. Such a ring will cover a too-large hole so that a smaller fixture can be used.
Another solution would be to plug the existing hole, refinish the area to match the rest of the ceiling, and cut the hole to match what is available.That might not be desirable... the following solution is probably the best:
I did find an 8" light (7 3/4" hole), and if you could enlarge the hole slightly (check for obstructions in the framing above) this should work. I am including a link to the fixture below. Even these 8" remodel fixtures (for LED) are rare (I only found this one).
Otherwise, I suggest going to a lighting center (NOT one of the big box stores) and describe the problem to them. They may have other fixtures available.
I am checking the "ready to be rated" box, but if these ideas do not work for your situation, please let me know and I will continue.