At PHL, parking isn't free. But there is a group of airport hotels all together (Four Points PHL, Aloft PHL, etc.) where one can park and take an airport shuttle.

The parking is gated but free for the first two hours, which should be enough time to take the shuttle, reach NK counter and buy tickets and return back on shuttle.

Maybe the same is there in Detroit?

I agree with the comments to be careful with Spirit on those once-a-year special vacation trips because of possibility of flight cancellations. I use ULCCs (Spirit, Frontier etc.) generally for domestic trips that aren't all that important.