Tom,
First I tried Steve's suggestion, but I had a "professional tire service" do it. One week later I returned to my coach in storage and the tire was flat. Upon calling Les Schwab, the professional tire service who did it for me, I was told I'd have to pay for the service call. A kid came out, "pumped up" the tire, but said he couldn't fix the issue so to come by Les Schwab. I stopped in, and I was blamed for wanting to have that done (Steve's suggestion) - it was my fault for asking - and I should have known there would be consequences - a possible leak. Well, I disagreed pretty strongly and wound up not having to pay anything.
So, then I went ahead and even though the tires looked great with only 20,000 miles on them (but 10 years old), I had 6 new double coin 606+ tires put on, along with, as Ed suggested, a set of new stems, one of which pokes out through a rubber grommet from the inner rear tires through the outer rear tires. I think my outers are both straight, though, just like on the front tires.
I then purchased the TST TPMS product with the flow through sensors so that I could air up without removing them.
The rear tire stems cost $120.00 I think it was, which certainly seemed steep to me and yes, you do have to have the tires off, but I was buying all new tires anyway. I forget what they were called but next time I go to the coach (Tuesday) I can find the receipt which should name the product if you're interested.
I've had only a minor issue with the rear stems in that I thought one (on the outer rear) leaked, but I filled it back up and haven't had a problem since.
Mike