Hearing loss runs in my family. When it's time for me, I plan to roll my own. I suspect that if you get rid of just one requirement, it becomes easy. That requirement is to stuff the whole thing in your ear. If the electronics can be in a separate box (or in a smartphone as mentioned), then analog, signal processing, and battery power all become trivial.
My dad is 81 and started having hearing loss a few years ago. He just sent me a pic showing the degree to which he was able to shrink his DIY hearing aid once he settled on the circuit design:
(Stereo mics and amp with two-channel parametric EQ on each side. About 6" wide and runs on two 9v batteries, if you're curious!)
He took it to a Bose showroom to compare it to their Hearphones. All (Bose people included) agreed that his amp and EQ was superior. Cost for parts is ~$200. He's had a lot of fun building them for himself and his friends.
I'd bet it'd be possible to make this much smaller and about half the cost. But I think it'd also end up a lot more difficult to adjust as needed since you'd end up with either tiny pots for adjustment or having to fix the values of everything and use single resistors. Going full DSP would allow you to make this fairly small and cheap (maybe the size of a 9 volt battery) but much more annoying to build and work on if you don't have the skill set. I'd bet this would be a good spot for someone to design a nice open hardware project that'd benefit a lot of people, and if it's setup as kits for headphones that just happen to work well as hearing aids you can probably avoid some of the regulatory issues even though you couldn't ever call them what they are.
Ideally, you need a mic and a speaker inside each ear so sound can be localized by turning the head. You can put the electronics and battery in a separate box, but wired is better than bluetooth/smartphone because it's hard to get the latency small enough with BT and a smartphone. (This is tougher with Android than IOS.) You don't want the direct sound leading the processed sound in the ear by more than a very small time. Probably single-digit milliseconds, IIRC.
I'm having a hard time finding it, but I learned a while ago that the Cochlear implant system went through a stage where the coil went to a small box worn as a small harness/backpack on the back.
One set of keywords that seems to turn up some of the limited info out there is "cochlear body worn processor".
Hearing loss runs in my family. When it's time for me, I plan to roll my own. I suspect that if you get rid of just one requirement, it becomes easy. That requirement is to stuff the whole thing in your ear. If the electronics can be in a separate box (or in a smartphone as mentioned), then analog, signal processing, and battery power all become trivial.