Here’s my view T (so yeah, some will disagree because I don’t use a fish scale when I put the cap on the valve stem

)……
Forget about tire height for a moment. Now, while I have never owned Secondairs, I have wheeled with Tirelocs for about 4 seasons. The Tirelocs run a second valve for the bladder (most know this already) and they get aired up first to a higher psi than the tire. The tire then gets aired up. While you may airdown to 9-12 psi, the internal bladder, at least with the Tirelocs, does not get aired down less than 28 psi. This is what helps lock the bead. I have aired down to 3 psi just to see what would happen, but a heavy truck like the 80 simply rests on the rim and you’d damage the rim by trying to wheel that way (yeah, pretty common sense, but just fyi). To me the main benefit of running the beadlock comes when you’re sitting there offcamber, with possibly all the weight of the truck being held by one bead…. Should that bead let go, well, you may be going over (remember that pic of my 80 with 3 winch lines attached to it – the only reason the truck didn’t go, before the cables were on it was because I had the beadlocks).
How much height would you lose? Tough call and depends on the tire etc. Think of it this way though, if you would normally airdown to 15 psi, but now go to 9 psi (giving you better pull over the obstacle), then the only difference in height would be the amount between 9 psi compared to 15 psi – pretty minimal height, and in my view substantially increases the traction you can get (yes, have gotten over obstacles at 9 psi that I could not do at 15 psi).
All of the above is based on experience with running these combined with bias ply tires. If you are now adding the radial variable into the mix then I’d have to question the combination of beadlocks with a radial tire. A radial will not have the sidewall strength that a bias tire has. So to me, I would rather have a set of street radials and a set of bias ply trail tires even if this meant there was no cash left for the beadlocks. I do not think that radials and beadlocks combined, so that you could run one set all the time, really makes sense – but again, just my view. I know you have reasons to consider this, but I just don’t think I’d go that route.
Now when you get into rim size you have opened a whole ‘nutha load of variables about the sidewall and sidewall roll/fold etc. I’m tired of typing
