I have some problems with adhesives, not the extent it sounds like you do, but here's what has helped ME at least:
I never, never NEVER use alcohol wipes. They dry out my skin which makes it more "fragile" and susceptible to irritation. I got lectured by the last CDE I saw for not disinfecting first, but its my skin not hers and I've had only a few sites ever get infected. For me the threat of irritation is much greater than the threat of infection.
I'm also sure that my sites are happier if I don't put them on freshly showered skin. I like the day after a shower best, or at least a day that I didn't scrub with soap in the shower.
I've inserted sets through tape, but I did okay with the IV3000 for the most part so I didn't try others. I've heard of a couple people having less reaction to a hydrocolloid tape patch although I'm not sure how well you could stab a pod through. I know if you ask Amazon about tegaderm and then check all the recommendations there's a lot of other brands that show up- Duoderm, Blenderm, Convatec.... Tegadem and IV3000 are the most commonly used which is why all the pump companies suggest them, but there's other tape options out there.
I take an antihistamine daily for other allergy issues( the generic zyrtec, which for whatever reason works way better for me than the generic other ones, and I get it really cheap at Sams club OTC, like 300 for $25), but its helped cut down on the irritation from the tapes too. For me one pill a day is worth stretching out a site for another day or two without mass irritation!
I've dabbled in lots of different site prep wipes- some worked better than others, but it might be worth trying a bunch of different kinds before throwing in the towel. Same deal as the tapes, put "skin tac" into Amazon and check all the related recommendations- skin prep, iv prep, mastisol- all slightly different. I got tired of having extra steps though so I never followed through to figure out which one worked best for me.
Not relevant to podding, but I recently switched to the metal sets and its made a nice difference for me. What I found out the hard way was that half of my adhesive reaction wasn't actually the adhesive, it was the infusion set. I don't use them exclusively because I can't figure out how to get them behind me without an inserter, but having thrown those into the mix seems to make the plastic ones (when I do use them) happier than they used to be.
And now, not relevant to the original post, but in response to the Ring of Irritation on the edges of a site.... I finally showed my Dr the scars from the blisters I was getting on the edges of the tape I was using to hold a CGM to the back of my arm and he explained that it didn't matter which tape I used because its actually the tape pulling on your skin in tiny micro-movements that tears your skin apart and in a bad spot turns into what looks like a bad rash or can even blister. The solution to that was some of the skin prep wipes, and me just getting a handle on which skin was to thin to put tape on. If its just on the edges, it not an allergy, its a 'thin skin' issue! Who knew?!
Good luck!