Next step: air dam.
I saw on a Miata forum, that someone had used paver edging to build an air dam. It was about the right depth and is nice and rigid. I also looked at a garage door seal that is popular for doing the same thing, but I'm pretty sure it would deflect which would defeat the purpose.
I pulled off my bumper last night and got to work. Here you can see it attached, as well as an unmodified piece of the edging.
There is also a new upper grill ($20 shipped off eBay) with a coroplast grill block. It's a very poor fit, but it will do. This is also new tonight. The edging is held in place with 1/4-20 screws/nuts with fender washers. Since it is so rigid, this only works because the bottom of the bumper is flat.
There is also a lot of damage to the underside of the bumper, and this helps reconnect a lot of the pieces and stiffen it all up.
And here it is on the car:
Not bad for $30 total.