Hi Erik,
I would role out the software issue since the factory reset didnt help you and because the problem appear progressively. It looks more like a faulty part that was dying.
I think it maybe your baseband or Wifi IC chips. Or one of the components that are related to thoses chips.
Aside if have High soldering skills and good equipement (mostly a good microscope), I dont recommend that you try to repair this yourself.
You can ask Jessa from iPad Rehab if you live in the US. But I not even sure that she we be able to help you since it's a somewhat uncommon issue.
Max One