Greetings, and welcome to the headphone community. I dove into head-fi in 2015 when I moved to Japan. I too, have listened to many headphones on the market.
The previous two suggestions, the Woo WA5 with Sennhieser HD800S is a very good suggestion along with RAAL SR1B. I have listened to both many times. Both come from two opposite sides of the spectrum to reach what you are looking for. I would definitely do your research and listen to the RAAL system prior to purchasing. This is not a HP you buy unseen. As far as the HD800, yes I truly believe paired with Woo products decreases the brightness and provides a very good listening experience. Personally, I would not purchase the HD800S unless you pair it with a warm sounding tube headphone amp like the Woo. I believe both HPs will work fine with hearing aids specially the RAAL since you can adjust the wings.
Now, let me throw in a 3rd suggestions, which will provide you yet another polar spectrum close to your price range. A electrostat system consisting with the Blue Hawaii SE (BHSE) and electrostat HP of choice. I am currently a proud owner of the BHSE with the Audeze CRBN. This system will run you 10K, but you can shop for a HP within your price range such as the Stax 007 Mk2. Now, electrostat system naturally is notorious for being analytical specially pairing with Stax, hence why I own the Audeze CRBN. Although, with the BHSE you can swap out tubes as needed to reach your desired listening pleasure.
https://www.headamp.com/products/blue-hawaii-se
The HeadAmp website will provide you info on the HD800S, RAAL and the BHSE with electrostat HPs. Not sure you location of residence, but I would recommend visiting https://thesourceav.com/ in Torrance CA. This is one of the few places where you can listen to all three suggested systems. Spent many hours in that place.
Good luck, and again welcome to head-fi.
P.S. If you ever come to the decision to purchase the BHSE/CRBN combo, speak to me and I may cut loose my personal system for your price.