Put a 38mm idler shaft and bearings in a 34mm case

Seriously, totally doable with the right parts. We ship a set or two a week that way.
I tell people all the time, choose the cleanest, lowest mile case you can find. The 34 - 38mm is negligible for most particularly for the earlier 38mm cases that still use a bushing in the output gears versus the later 38mm with bearings in the output gears (truly better with the bearings). I run a 34mm behind the H55F in my FJ40, have for several decades now. Many broken birfs and rear axle shafts, t-case is fine. It is getting noisier with time, I'll eventually swap a 3:1 or 3.3:1 variant in there.
There is some ongoing discussion that the 34mm cases have some thinner aluminum in locations, I don't disagree but need to spend some more time with them side by side. Perhaps you could weigh the two cases half pairs you have and see if there is much difference? Advance adapters for example won't machine the 34mm cases for low range gears unless they've added additional material. Our machine shop prefers material on both cases so? I've got variants of both here in the shop and just haven't measure those thicknesses yet.
...However, who here has seen a 34mm idler bearing wear out?
Me. It's not the bearings so much as the 34mm ilder shafts themselves do seem to get far more wear (grooves) in the same relative mileage as a 38mm, that is obviously the trend Toyota was correcting with the increasing idler shaft size of the years. It's not so much a strength issue as a longevity situation, I have no doubt the 38 idler will stay tighter in the same 250k miles of service due to the shaft surface area and subsequent larger bearings surface. Poor aftermarket idler shafts exaggerate the situation, we've had customers need to replace their Chinese or Indian idler shaft as the hardening was obviously not up to par and it left them with a noisy t-case. Unfortunately this was common a decade ago. Less of those kits in the US now, most have good Japanese shafts in the kit.
Also there was an "important" change to the post '85 transfer case- the oiling provision cutout to snap in the plastic oiler for the 5 speed. Since a new casting needed to be made to do that - they likely threw some other things into the to-do list as well (larger idler & bearings etc) since they weren't expensive changes.
The oiler cup provision absolutely exists in 34mm cases after ~10/82' fwiw.
Split-Case Versions
8/80' - 10/82' - 34mm idler shaft, unique input gear. No oiler cup provisions. No spacer bolt hole.
10/82' - ~83' - Same as earlier case, with updated input gear. Introduction of oiler cup provision at this time. Middle bolt hole not present.
~83' - 4/86' - 34mm idler shaft. Has oiler provisions. Has spacer bolt hole.
4/86' - 8/87' - 38mm idler shaft. Has oiler provisions. Has spacer bolt hole.
8/87' - 1/90' - 38mm idler shaft. Auto tranny version. Vacuum 4wd. Has oiler provisions. Different gear train, bearings and seals than earlier 38mm cases.
4/86' - 90' - 38mm idler, no oiler (might have been an auto one I had without oiler provisions?)
This doesn't include the many non-US variants out there. At best guess there are 20 different Split Case's used by Toyota?