If it is a single stack 1911 22 conversion kit I think you should be able to find a mag that will work with your Tactical Solution kit.
I just found this thread on rimfire central and it is worth reading. Here is a quote and a link.
I took my Tactical Solutions 1911-22 out and tried my Armscor XT-22 magazine in it. Worked fine! Also tried a Ciener Conversion mag, all worked fine.
https://www.rimfirecentral.com/threads/1911-22lr-magazine-interchangeability.571261/page-2
I have three Kimber 22 LR mags I use with an EAA 1911 22 LR conversion. I could send you one so you could test it.
Greg Cote llc has RIA XT22 mags in stock and they look very similar to the Kimber mags.
https://gregcotellc.com/cart/armscorrock-island-actmag-c-152/armscor-rock-island-armory-full-size-1911-xt22-10-rd-22-long-rifle-magazine-55089-p-1806.html
Here is a picture of a couple Kimber mags with the EAA conversion kit slide. Just for comparison, I don’t have access to a RIA XT-22 to test.