Pyrex CRTs present special problems. Apart from the higher temperature needed to work Pyrex it's likely that a soft glass pinch will need to be used. There are no new Pyrex pinches and re-using the old one has been regarded as not feasible. Though I suppose that could change if driven by desperation.
You can't fuse pyrex directly to soft glass as the differing coefficients of expansion will ensure the result will crack. Hence you need a graded seal, with several intermediate grades of glass between the pyrex and soft glass. The special glasses are available but it requires a high level of glassblowing skill to do it. My understanding is that RACS subcontracted that part of the work.
I haven't studied the structure of guns in detail but I think there are 2 main ways they were assembled. Older ones were spot welded while newer ones had their elements fused into glass rods. The former can be dismantled with appropriate skill and care, the latter can't. I hope that the HK assembly can be removed from later guns without the need for extensive dismantling.
As for cleanliness it's just commonsense to keep things decently clean, even if oldtimers' shops were a bit mucky. The only rebuilding shop I've seen was Display Electronics, near Heathrow airport. This was fairly mucky but they turned out good work. They didn't do any work on guns, just fitted new ones as was always the case back then. The 6/6 they rebuilt under my direction in 1986 had its gun rebuilt by (long defunct) Thorn-EMI Electron Tubes. As others have said, there is no dirt problem when pumping and baking the CRT. the muck is outside and the vacuum is inside. However a tiny speck of dirt in a gun assembly will likely cause trouble. Hence if the oven is in the same room as the gun rebuilding then the whole place needs to be kept clean.
We're not talking about microchip fabrication here, no need for clean room facilities, but it's always easier to make a clean place dirty than a dirty place clean
