I have looked hard for a better tire for concrete then the TPU I have been printing. Still no luck. But, I may have a simple solution. I will it cover here with a few images.
The quick test run on the concrete in the dark was much better than I was expecting. This may be what I end up with in the end. The good news is the bands are less than $10.00 for 30 of them so tire cost will be pretty low.
In fact a rim and tire as one unit may be printed in PETG and a cap added so TPU may not even be needed. I will report back on this later.
Now with what I have so far:

"A" My TPU tire
"B" Skog Bands: Heavy Duty Rubber Bands Made from EPDM Rubber - 5col Survival Supply (Medium)
"C" Place a band centered on the TPU tire.
"D" CA glue one edge of the band to the tire. (here I clued the left edge)
"E" Then roll the other edge back to get to the center of the band and run a small bead of CA glue around the center of the tire.
"F" Roll the band back in place and once the CA glue dries the tire is ready for some hot laps to scuff it.
"G" Once the tire has had a few laps it is ready for the big race.
Scuffing the tire (running hot laps) removes any CA on the outside of the band.
Below are closer images of the steps I take to mount a band on a TPU tire.
Roll the cap back in place and remove any CA glue while it is still wet. Let the CA dry before scuffing in the tire. (Running a few hot laps)
The first run of tires I printed were smooth across the top.
I am going to create a tire that has a slight step where the band will set to make it easy to locate the band on the tire for gluing.
The bands I am testing are made from black EPDM rubber, an extra tough material that is stronger and less stretchy than regular rubber bands. They are called "Skog Bands".
The EPDM rubber used in Skog Bands provides excellent durability, with strong resistance to UV light, moisture, heat, and cold. EPDM rubber is also used for applications like commercial roofing, long-term resistance to environment conditions is mandatory.
The bands I have are not very thick so not sure how long they will last but they do seam to be tough and they also have a lot of grip. I will report back when I have more tire info to share.
If you know of a source for a 1/18th scale foam tire let me know as I sure would like to use something off the shelf if it is out there.
I have more updates on this project coming soon.