I started wearing hearing aids myself to amplify the sounds in the upper frequencies so I can hear the consonants in words, so I understand why you are looking for more warmth to tame the hearing aid's reproduced treble.
By the way, you may want to mention hearing aids in your title to see what suggestions those already wearing them might have.
You may have tried these adjustments, but my hearing aids have a phone app to change programs and make EQ adjustments. There is a “Music” program that takes all the noise suppression and voice enhancement processing out of the circuit for just amplification of the signal, so see if your’s have something equivalent. Mine also has a 3-band EQ, and trimming the mid and high frequencies can help. Also, try lowering the hearing aid’s volume to better integrate it with the “natural” sound from the speakers.
Finally, the type of ear dome you have will make a difference. The more “closed” (vs. “open”) its design the less natural sound comes in, making both integration of the natural sound and warming of just the hearing aid’s upper frequencies more difficult. (But what type and amount of hearing correction you need will often determine the best dome.)
Bottomline, a hearing aid is a full audio production system; microphone, analog to digital convertor, preamp/hearing aid processing/AI, DAC, power amp and speaker reproduction. You’ll only get so much sound quality out of something doing all that and be small enough to sit behind your ear (mine’s an RIC).
Since I don’t know what your hearing aids are helping to restore, the following may not apply. Without hearing aids I can still hear up to 12K hz and easily distinguish subtleties in the upper frequencies like whether a ride cymbal is struck on the edge or bell, difference between a violin and viola, etc. While the brain does a great job of filling in sounds from memory, I can still retrieve those sounds, but they sound rolled off and recessed because I have mild loss around 500 hz progressing to moderate at higher frequencies.
If that’s similar to what you have and there’s times you listen to music alone, then I highly recommend using EQ with your system and listen without your hearing aids.
In my case a Schiit Lokius or fully restored SAE Mark Seven work very well as I prefer listening to my stereo without aids for the best quality, resolution, and soundstage. With aids, even in Music mode, there was always some digital hash in the treble and a sonic hole between the lower natural and upper aid sounds. I even have open style ear domes which helps. When other’s are listening with you and/or you have your aids in, just select “bypass” to take out the EQ.
If you want/need to listen with your aids, then I agree with those who have recommended tubes for their proper harmonic frequency emphasis and low damping factor.
A preamp, like grk suggested, can have the most effect on the signal. For preamp tube rolling, English tubes like Mullard’s lean toward the warm side.
For power amps, I agree with @jasonbourne71 and others recommending the Dynaco ST-70. I have one with the Bob Latino VTA mod with upgrades and it’s a great tube sound through high sensitivity, two-way speakers like yours (mine are a modified Altec Model 19). The center tube provides the most sonic difference in the front end. For power, EL34’s are more warm than 6L6’s, though not as dynamic.
For an even richer, sweeter sound, a single ended amp, especially in ultralinear, could be what you prefer. Mine, an Elekit TU-8800, or its successor the TU-8850, are options if you’re a DIYer or find a nice completed amp and want a wide range of power tube options. Either way, go with the Lundahl transformers. Ready-made options with good reputations include Decware.
FYI, I ran a Crown XLS 1502 class D amp (some give it good marks for stereo listening) while modding my tube gear, and it was pleasing with tighter bass and resolved, analytical highs, but did lack the fulness and warmth of tubes, so you are on the right track with the First Watt amp. I have no experience with Pass, or First Watt amps for comparison, but First Watt is certainly proven.
Something to consider regardless of your audio gear is the listening room. Your hearing aids are reproducing frequencies in the range that includes mid/hi sounds that are part of first and second reflection points, so the audio distortion those reflection points produce will be enhanced as well. I’m lucky enough to have acoustic treatments at those reflection points and they make a very big improvement. If you can’t do the same, consider what speaker and listening placement, furniture, bookcase, etc. changes you can make in that area as it will improve any system you go with.
Good luck in finding a solution that works for you.