Hi "Wetboots"
This does seem to have turned into the proverbial can of worms.
As for the solenoid not providing any protection against backflow, I do believe that depends on their being some signficant positive pressure and water supply (both factors) in the irrigation lines in excess of that in the potable water system. I mean, I don't think the solenoid is a wide open sluice gate for backflow. However I suspect you are correct that they are designed to hold off a head of pressure coming from the supply line, not (certainly not) the other way around.
Certainly, it would benefit us to keep a close eye in the near future on any use of the fire hydrants (one's right in front of the house) that leads to significant depressurization of our potable water system. The township does drain these annually, but I never paid attention to this before... nor have I seen any dead animal carcasses.
I don't know whether the home *practically speaking* is unsaleable since we bought it in that condition with the help of an apparently assiduous and honorable -- certainly hardworking -- inspector. [

] Perhaps the right statement rather is that it should be unsaleable without a PVB valve but this might or might not be caught by the next buyer's inspector should we ever sell the place.
You are correct, however, on the issue that it is something that must be dealt with. What I'm left to wonder is whether the sprinkler system was properly permitted originally. That is a potentially significant issue. Since a major renovation was performed at that time and many many drawings were filed with the local government, it's hard to believe that it wasn't inspected then. BTW there is an older irrigation timer located next to the electrical panel (also Richdel as is the currently functioning timer) which has been disconnected but not removed. Hard to say what that signifies other than that there has been a long-term use of a sprinkler system dating back more than a few years before we bought the house -- i.e., odds certainly are that it was here at the time of the major renovation. Furthermore there are lines going underneath the driveway and that has (from its condition) not been replaced for many years.
But if not, there are other issues to be concerned with here. You might or might not be aware that permits and inspections are critical to satisfying the homeowner's responsibilities for insurance coverage -- this is not a trifling matter, not at all.
Interestingly, the AVB is all-plastic construction; I guess a PVB also be all-plastic. E.g., the Toro model 53300 (a PVB shown at their website) does appear plastic. This could make a significant difference in whether I am replacing like for like (and therefore do not need a permit) or am installing something new.