Your calves are sore because of the change in heel drop from 12mm to zero in spikes/flats. Your arches are sore because of the lack of arch support in spikes/flats. There are two nearly opposite approaches to this. One is to strengthen your foot. The other approach is to support your foot.
I'm much older than, well, pretty much everyone on this board and I have many chronic foot problems, so I choose the latter approach. Thus, my solution might not work for you. That said...
Get a lower heel drop shoe for your normal trainer. A 12mm drop promotes heel strike, which you can't do in flats/spikes. The change from 12 to 0 is part of the reason why you have calf issues. Personally, I prefer a neutral/performance shoe with a 4-6mm heel drop and a Superfeet insert to provide a little extra stability and arch support for my road runs. My training shoes typically weigh 9 1/2 ounces. You might still do your longest runs in the Adrenaline.
Also, once my spikes/flats are broken in, I don't run in them unless it's a race or a time trial. I also choose my spikes/flats to have a little arch support when laced up. These are the models that curve in a lot at the arch area of the shoe. I do my interval workouts in a performance shoe that has more cushion and arch support than a flat. My interval shoes typically weigh 7 1/2 ounces.
Finally, I run barefoot on the grass for my cool down run. This is the strengthening part. You need to start with very low volume and build up... maybe only 200m at first and building up to 1 1/2 miles over 12 weeks or so.
I typically have 5-6 shoes in my normal rotation: a long run shoe, a long run/interval shoe, an interval shoe, two pair of trail shoes, and then my racing flats and spikes.