Thought I would post an update here with the final outcome of all the tire ruminations.
We came very close to buying the Bandags. What ultimately nixed that idea was the Bandag guy himself, who basically told us that he would not stand behind the tire if we were going to run it at 90-95 PSI -- he wanted to see at least 110 PSI in the tire.
Well, that defeated the whole purpose of switching to the 315/80R22.5 size. At 110 PSI, the 12R22.5 tires we've been running are more than adequate to support our load. The idea, for us, behind switching to the larger size was to run a lower pressure to help with loose surfaces such as sand and mud. (And, yes, we do park on the beach, and we have been through plenty of mud, getting stuck once.)
Furthermore, one of the tools in our chest for dealing with soft surfaces, which we have thankfully never had to use, is to lower the pressure in the drive tires if needed, as any off-road enthusiast will tell you. Manufacturer load and inflation tables allow a substantial drop in pressure (or increase in load) at extremely low speeds, and we could conceivably drop our tire pressures to 70 PSI or even lower to get out of soft stuff, then use our on-board 150 PSI compressor to re-inflate to normal pressure before resuming driving speeds.
With the advice against running the tire below 110 PSI, we felt that we'd be more nervous doing this with a re-treaded 315 than with a virgin tire, even the 12R.
After we ruled out re-treaded 315's, I went back to the phones to try to find open-shoulder drive tires in either size. 315's were extremely difficult to locate, and I was not happy with the couple of patterns we could come up with. The tires I really wanted in that size, Goodyear Regional RHD or Continental HDR, were unavailable. Even the Michelins were scarce, assuming I wanted to pay $660 a tire (gulp). To top it all off, on virgin rubber, the difference in Federal Excise Tax between the two sizes came to $25 per tire.
Once we regrouped and converged back on the 12R22.5 size, which itself was scarce in our tread pattern, we decided to again evaluate the Bandags, looking at capping our existing casings. That would have had us on blocks at the tire shop for three days, plus my casings are DOT 1304, making them five years old this month -- we'd only consider running them for another year or so, at most.
In the end, I was able to locate a set of four Bridgestone M711's, the very same tire we were already running, with 4708 dates. Way more money than the Bandags, but I am confident I will get another four years and 80,000 miles or so out of them, which is what the last set gave me.
We also switched out our cupped Goodyear 315/80R22.5 steer tires for a pair of virgin Firestone FS560s in the 12R22.5 size. I won't run recaps or used tires on the steer axle, but I was darned if I was going to put another set of $550 tires on an axle that has demonstrated a propensity to cup tires in a mere 20,000 miles or so. At least not until we can cure whatever is causing the premature wear.
Total bill, with six tires, FET, CA state tax, mounting, and two spin-balance (steers only) came to $3,400. Of that, the drivers were $486 apiece, plus $36.76 FET. I think capping my existing casings would have run less than $200 apiece, and no FET at all.
Posted to inform (or appall, as the case may be).
I'd like to thank everyone who took the time to post their advice here. I think, had circumstances been just a bit different, we may well have gone with the re-treads. In fact, we may look at re-treading this set in about three year's time, before they are worn to the belts and when they still have a few years of casing life left. And I am certainly going to look into re-treading the tag tires when they wear out, or at least trading them for re-treads on clean casings.