Update: So, I used these under-sink mounting clips, designed to hold up a household sink under a countertop.
https://www.amazon.com/dp/B0878Z7Z1F
After trimming the sides of some of them for the front and back of the sink, I epoxied them to the underside of the sink using PC-7 epoxy (see below photos). After it cured, I mounted the sink using the wing nuts that came with the brackets. Took about 20 minutes to get all the screws, as compared to hours using the OEM method, which also didn't work well.
If I were a manufacturer, I would be finessing this solution, like cutting the brackets a bit to make them shorter (particularly for the two brackets on the front middle of the sink) and making the bolts longer. But ultimately, this solution as is ended up working out great. The sink is more secure than it's ever been in the ~15 years I've had the TM, even after a road test on a 3-mile long dirt road in pretty rough shape. Cheap, and far easier and more effective than the OEM method (and by OEM, I mean by both TM and the sink manufacturer.) Hopefully the success continues.
Dave