A MAC fits inside of this, so its diameter will be smaller. A MAC was originally designed to replace a Trident II D5 ICBM in an Ohio sub's missile tube. The dimensions of a Trident II D5 missile are shown here:
One MAC holds 7 Tomahawk missiles, so the 7 of them, plus the MAC itself have roughly the footprint of a Trident II D5. A Virginia Payload Tube is described as being able to hold a MAC, yet carries only 6 missiles instead of the 7 in an Ohio's MAC. So, "something's off" there somehow. I suspect a VPT is a bit smaller than an Ohio missile tube, perhaps? I consistently read that the new VPM will hold MACs with 7 missiles each, to be coupled with the six each which the subs will also carry in their bows, so it appears tubes centered around MACs, not VPTs, is more properly the focus. There seems to be more of a difference than I originally understood between them. You found an 82 inch VPT diameter, and I am getting 87 inches...that looks like it right there, maybe? One's a VPT, the other an "Ohio" MAC for its tubes.
A useful article:
It explains that an earlier MAC concept of a decade ago would hold three intermediate range ballistic missiles. They are dusting that off, so "three" looks like the "magic number" planned to be fit in a current MAC system.
Not as definitive as I had hoped for when starting my search, but "things to add" to the "clue pile."