An update: over a period of a couple of weeks I have successfully migrated my original 4x4TB to a 4x10TB (well, technically 9.4TB each). I was too lazy to go through all of the renaming, so I figured I’d go with remove and add for each of the drives … well, I think a backup with a straight up replacement would have been way faster, even though I would had to maneuver through the obstacles that @phillxnet had laid out.
I started with adding a new 10TB drive to ensure I would not run out of space, and the subsequently did the remove/add/remove/add, etc.
Each remove action and add action took a little over 24 hours each 
and we’re talking about 8 TB total data across the RAID …
I almost screwed up by removing a drive that was still being “removed” in … fortunately, this test showed me that even a RAID 5 on BTRFS can recover from such a dumbass move. As far as I know I have not lost any data (a scrub told me so, and I did a rough comparison to my backup), but who knows…
I also moved over to a RAID10 setup now as part of that. I have not had any issues with the RAID5 since I started using RockStor, but I’ll try the RAID10 for a little bit to see how that goes.
So, thanks everybody for the tips, I still made it the most drawn out process, but it’s done for now. Now what to do with the 4x4TB drives … maybe build another NAS/off-site backup …