Well, I'm heading to south GA in a couple of hours for a weekend of deer hunting. I'm also bringing that "often posted about" 308 Ultra back to it's owner. No, I didn't send it back to H&R because of the lateral play yet, even after Gordon told me to a couple of weeks ago.
Seems like what I did do is buy a 270 barrel from the classifieds. I kept the Ultra until it arrived because I couldn't wait to check the fit. It mates up to the receiver exactly like the 308 barrel; some amount of lateral play with the forearm on. Both barrels will lock up on a .0015 shim, and I can't pull the shim out of the closed action, which is strange considering the amount of "slop." But what do I know...
So I get an idea. I put a shim between the spacer and the wood on the forearm as Tim (I think) had once mentioned. Lo and Behold! Lateral play is gone (only with the forearm on of course).

Obviously not a barrel to breach play fix, and it does increase the forward pressure on the fore end retaining lug I worked so hard at eliminating, but it
feels nice and tight.

Maybe it's owner will want it back to play with and I can get back to my own Handi's!