Apparently the correct term for those clips is "U-nuts".
A quick Google search netted me the following info:
Mopar Part # 00152493
Available here for $5.50 for 4 clips:
https://www.viperpartsrackamerica.com/index.php/products/2003-2013-dodge-viper-srt10-u-nut-00152493
It's apparently a common part that's also been used on Dodge Rams:
https://parts.chryslerjeepdodgecityofmckinney.com/p/NUT-Front--Rear-Extension/42148528/00152493.html
Clips and Fasteners has many of these U-nuts that fit #10 sheet metal screws:
https://www.clipsandfasteners.com/u-clips-nuts-and-fasteners-s/115.htm?searching=Y&sort=13&cat=115&show=45&page=1&search= #10
These look like they would be a pretty darn close fit:
https://www.clipsandfasteners.com/10-Screw-Size-Wide-Range-U-Nuts-p/pas5752-50.htm
$5.99 for 50 of them is a little more like it.
I removed one of the screws + clip/U-nuts from my belly pan:
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The screw threads are ~0.190" in diameter (peak-to-peak), so they appear to be a #10 sheet metal screw. The screws are 0.75" long (under head length). The captive washers are 0.6110" in diameter, and are 0.047" thick. For reference, the screw head diameter is 0.4865", so the washers aren't all that much wider. The screws take a #2 Phillips head screw driver.
All measurements were taken with my digital calipers.
Here are the U-nut dimensions:
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From my rough measurements, it looks like it could accept up to a 0.1550" thick panel. Again, the U-nuts linked above would be a pretty close fit.
The U-nuts likely aren't there - they attach to the carbon fiber belly pan. If the belly pan isn't there, the U-nuts likely went right along with it.
Hopefully that helps at least some.