Is this the sign? Or are there actual ways of measuring rim wear?
It's not
The Sign, but is an indication of quite a bit of wear.
There are ways of measuring remaining rim thickness, which is what matters. Biggsy's suggestion is a good one. Alternatively, if you have a pair of vernier calipers (or even a micrometer, which I don't own) , you can bend up an old 2mm spoke to fill up the hollows on the inside & the outside of the rim (due to the hooked tyre bead retainer inside & brake wear on the outside). It's something I've picked up from an article by Chris Juden in CTC's Cycle magazine, but I can't find an an online reference, & couldn't in in 2010. If you need an explanation, I'll do my best to explain how to bend the spoke.
Chris concluded that failure occurred typically with a rim thickness of 0.7mm & advised that it would be unwise to ride with a thickness less than 1.0 mm.
I have no idea how thick Shimano RS10s are. I tend not to believe what others say on this subject without doing my own measurements. I found Open Pros had always been a lot thinner than others believed (consistently 1.3mm vs a claimed 1.6mm). I still use them, but only with a (mainly) leg-braked fixed wheel.
You don't seem to have a lot of time to sort out this one before the Dartmoor Ghost and, without resorting to the hype of some previous contributers, getting it wrong has a risk. If you have space to store a spare rim/wheel or 2 (and are not strapped for cash), I'd suggest installing replacement(s) for the ride & working out whether it was really necessary afterwards.
HTH