I have worn aids for many years (over 40), and can appreciate the changes in technology. Unless your loss is straight-line, and most are high-frequency, you will loose accuracy if you either take them out to use a headset or buds.

I have the same problem with feedback noted with the over-the-ear cans, but I found a headset that works for me. The Sony MDR-ZX330BT is about mid-way in size between the big cans and one of those flat jogging headphones, and I get no feedback from it. It's bluetooth capable, so you can put a small bluetooth transmitter next to your source, and not bother with a wire tethering you to it.

Another option, if your aids have this capability - some newer ones do, some don't - is a direct bluetooth feed to the aids. This may require a special black box designed to work with those particular aids. I have one, and I find its battery lifetime is very short (2-3 hours) when used for listening to music, but the sound response is terrific.