I see the plan is to make towels but wonder if the fabric can be firm enough for a placemat?

It could be firm enough for placemats if you increase the sett quite a bit. Because the episode isn't out yet I cannot give you the exact time stamp to watch for, but I do go through a series of sett samples and talk about what they might be good for use-wise. What you're looking for is the bright orange and magenta pieces of fabric. You can't miss them, they are eyeball searingly bright!

The sett of 24 epi/ppi is firm but not quite placemat firm. They aren't thick at that sett either. This is definitely more of a dish towel yarn combination than a placemat one, in my opinion. If you are okay with thinner placemats, though, I'd suggest you sett sample, starting at 24 epi/ppi and going tighter from there. Sampling will tell you what you need to know, and there is plenty of yarn to do so.

But do give the episode videos a watch when they release, you might decide the dish towels are worth making after all. They're so much fun, and really thirsty!

If you did DPW with 8/8 cotton as pattern and 8/2 or 16/2 for thin tie-down yarn that would be a better fabric for placemats. Nice and thick, yet still washable.

It's great that your 20 year old rep weave placemats are still going strong, but I certainly understand the need for something new. Having options is the best scenario!