Find another sheet rock installer who will add what is needed. The crew you had are just simple installers, not wanting to do the difficult small problem areas.

ditto......

Amazing that such a simple problem has "professionals" stumped.

Amazing that someone chose insect infested firewood to place in their home as a STRUCTURAL element. It should have been heat treated, and used decoratively OVER the drywall, if it were used at all.

How do you know it wasn’t heat treated? And how do you know it is insect infested? Do you ever have non caustic opinions?

I don't think there are any stumped professionals here. The existing situation is a simple one.

At this point, given what the OP has said about no trim, the only option is to scribe gyp board panels to follow the contour of the old wood as closely as possible, and thereafter to carefully caulk the gaps before painting. This will involve removing the existing gyp board panels and reinstalling new, scribed panels. This will be labor intensive and expensive.

This application, as Sophie says, should have had all the gyp board installed before installing the old wood beams, so that there would be a continuous ceiling plane without joints, cracks or voids.

With scribed gypsum board panels (and no trim), it's very likely that there will be seasonal cracks and openings over time, each year in the ceiling. That's because it's likely that there may be seasonal differential movement between the old wood beams, the adjacent gypsum board panels and the supporting ceiling/floor joists, which may lead to cracking and separation of caulked joints.

And, the biggest issue of all will result from that design: air infiltration from conditioned to unconditioned spaces. That will lead to energy inefficiency, moisture problems, insect travel paths, and a whole host of other issues that could have been avoided with proper design.

A lot of people hang sheetrock and get paid to do that. That is technically professional.They specialize in doing a level one(garage/unimproved interior spaces) or level three(ready for finishing) installation normal for the average building. They are fast and competent, emphasis on fast.

I've taught volunteers to hang sheetrock and gotten complements from the mudding crews on the installations. The volunteers were not fast, but their work was very good.

Then there are folks who can do a level 5 sheet rock/mud job and do that fairly quickly. I can do a level five job---takes me twice as long.

That is all new build work. This situation was new build planning done badly. As Sophie said, the sheetrock should have been done first, then the beam if a new build crew were used. Otherwise, a remodeling sheetrock crew should have been selected. There is a difference is speed/skill set between the two.

I too want to know how that photo indicates to Sophie that the beam was not heat-treated, and it's insect infested. I want to know how to identify those things in wood, so that I won't make those mistakes. Please let us know how we can tell that.

What one can immediately see by looking at the beam in the photograph is that it's out of alignment in the x-, y- and z-axis. It's twisted in three different planes. From the outset, there was never any way that it was going to align with any normal construction materials and processes.

Why it was installed before figuring out that there was a problem, and how to best solve it, is the real question.