So, the valuable lesson to get from here is to never use pinned blueprints until you are at grade 5 with that engineer. It may be a bug, but you can easily avoid it just by maxing the engineer first. Am I wrong?
It's possible I'm mis-reading, but do you know that the grade has to be unlocked with the
engineer via reputation? If you haven't gained the reputation with Broo (for example) to unlock Grade 5, then you will not be able to upgrade modules to Grade 5, this is a lock on the engineer, not the engineered module. Remote engineering does not increase reputation with the engineer, you actually have to go to the base and do the engineering. It sounds like this is what support are suggesting to you. Another possibility is to remove the engineering (anyone know if you can remove individual grades?) from one of the engineered modules and re-do it at the engineer's base, or for those engineers you can raise reputation with through other means just use that mechanism instead (e.g. selling exploration data to Farseer or Martuuk).
Edit: hand in bounty vouchers is listed as a possibility for Broo:
https://inara.cz/galaxy-engineer/15/
"Pinned blueprints" are not the issue here though, not in the context of this issue, they have their own problems though. I have been to his base numerous times with other lasers, and through "crafting modules" I've got to level 4 with Broo, but I didn't have the mats to get to level 5. I currently have 4 lasers at level 4, and 7 others at level 2 or 3.
The only reason I even knew there was a problem, my "pinned blueprint" for him had "suddenly disappeared" after the last update, as well as a few others with different engineers. So, I went to his base to see what was up with the pinned blueprint, and I see that my rep with Broo is level 4, which I knew.
At the other engineers where the blueprints had "vanished", I took the module I wanted to upgrade, had the mats, and was able to carry on from their current level, by "crafting modules", and finish them off at level 5, while also "re-pinning" the blueprint I wanted.
The requirements for Broo's rep gain are "Craft Modules", and or, "Hand in Bounty Vouchers". So, I want to continue on where I left off, and "craft modules" to get to level 5, as was suggested by Support. The problem is, I can't with any existing module I have. I'm going to have to start at level 1 with a new module, which was their suggestion, which is simply ridiculous.
I should be able to take any of my "unfinished" modules to his base, and "gain rep", by "crafting modules" and I simply can't. The only option available to me is start at level 1 again, yet I have 4 modules at level 4 already, plus a bunch at lower levels, that were upgraded "at his base", as he's the only engineer that does level 4/5 for lasers.
Hope that makes sense, I can't "describe/convey the issue" any clearer.
To summarize: I want to increase my "rep gain" with Broo to level 5, I'm currently level 4, at his base, "by crafting modules", using my existing grade 4 modules, or any that I have that are already started, and I can't. I have to buy a "new module" and start over from level 1.