TL;DR: seems to me you're leaning towards selling zhp and either: 1) keep cheap problem-free company lease and perfect weekend miata, or 2) consolidating and moving into a new(er) do-it-all car (will your company help with the cost of a do-it-all car?).
Long version:
I daily mine. It's been great, but I think that's because I went through and replaced many of the maintenance items (see my project thread for the list); in essence I "zero'd out" the maintenance for everything, thus minimizing the chance of unexpected failures so generally it's simply regular maintenance schedules for fluids and filters.
I did not do this with my previous e46 330i and was intermittently dealing with "old car problems," which became really annoying, time consuming, and tiresome. My tolerance for unexpected problems has been diminishing, also the "fun / hassle ratio" of wrenching seems to be diminishing as well. This is probably a function of getting older and wanting to do other stuff with my time. General maintenance is okay since it's planned. The unexpected stuff adds a level of frustration and hassle that's annoying.
But even with all the wear items replaced having multiple cars has it's potential downsides: storage, cost to insure, basic minimal maintenance so it doesn't "fall apart." It also lacks some of the newer car amenities which are just nice to have in a daily driver (mainly the peace of mind that if something happens I can get it warrantied at the dealer and have a loaner car while they work on it, rather than parking it unmoved until I have time and energy to diagnose and fix it).
My perfect combo was an i3 and my e46 m3. I drove the i3 most of the time (In 2.5 years: i3 had ~43k miles, while my m3 added ~5k miles). The i3 was close enough to a do it all car (albeit limited range, and no sweet sounds of a NA motor or the steering feel of mechanical power steering) that I didn't feel like I was driving an appliance.
Tough choice, but it sounds like you have some good options. The ZHP is a great car, but it seems like the post-grad school ones didn't capture that pre-grad school enjoyment / love. Maybe you're in a different situation now and see things slightly differently?
The bolded text below are what stuck out to me.
It sounds to me like you're leaning towards keeping the cheap trouble-free company lease and the miata as it's the perfect weekend car, or simply a new(er) trouble free car to do it all as you mentioned. Sucks that the loss of parking space is forcing the choice, but seems like you have good options to choose from. Good luck, keep us posted.