The "1st gen" SE is the same size as the 5, still available from e.g. Amazon for $100–$200, and runs the current iOS very well if a little slowly.

I ran those for many years but unfortunately the batteries are old and seem to only last a year these days

Why not go to an Apple Store, and buy a new battery?

running with 1st gen se since fall 2018: battery is still at 95%

replacement kit from ifixit is available thou

I pulled a 5 out of my draw and was pleasantly surprised at the size and feel, but then I actually went to use it and it was quite bad. I wasn’t able to comfortably two hand the phone to type which meant my typing speed was massively reduced.

Personally I mostly use my phone two handed so even the pro max is usable even though I can’t reach all areas with one hand.