Converting a Challenge into a road car, possible?

It wouldn't be hard to get it done at a Florida DMV. Someone bought a 1999 Dallara Indy car and put on those PIAA-type lights you buy from Autozone and put it on the car and made them functional. They were able to get a title and road registration. Here's an old article about it, but unfortunately the photos no longer are up: https://jalopnik.com/212912/street-legalish-indy-car-on-ebay

I remember seeing pictures of it driving along I-4 in Orlando in traffic.

FL DMV doesn't care. Just pay them the fees and they will OK it.

Edit: I just noticed your location. If you buy a vacation home in FL, you could do it.