As someone who works in Property Management in Washington DC I would say do NOT get a permit. The permit process in DC is very slow and cumbersome, many contractors are willing to work without them. No issues with zoning as your garage is not becoming a domicile and you are not running plumbing to it, if you have an HOA then check with them first. Hire an electrician to connect a new panel and run some outlets. You might be able to do the framing/drywall/insulation but I would hire someone to do it right unless you are experienced. I know some reasonable contractors, if you are interested send me a PM. I think the mini split system is the perfect option for heat/AC in a pinball garage. I would also add a dehumidifier and run it during the summer, these are cheap and easy to set up. I would keep the cement floor and see if you can paint it and seal it, I have seen some really cool garage floor art done in friend's houses and if sealed it really lasts.

The big question is the garage door. How old is your garage door? Are the seals on the bottom in good shape? If not can they be replaced? Do you have evidence of rodents in the garage? Is it an electric door or manual? Is it secure?

(Also I loved your book!)