The current description of the Headquarters reads: "The place where generals are trained for resources. Each level increases by 1 the number of levels a general can raise via training for resources."

This is misleading - it means that at level N of Headquarters, any general should be able to raise their level from X, where X is the general's current level, to X + N. Instead, the building only lets you raise a general's level from 1 to N. The Gubernatorial Headquarters have a slightly different description, but it also presents a similar confusion.

I would suggest revising the description, but a better solution would be to just make the Headquarters function the way the current description reads: If you have level 2 Headquarters, then you should be able to raise one Great Person's level by 2, whether that's from 1 to 3, or from 11 to 13. Then that same Great Person can no longer increase their level using resources until a new level of Headquarters is built. Of course, this makes the building a lot more useful, so the resources required to go from one level to another should be proportional to the starting level.

Otherwise, the Gubernatorial Headquarters in particular are almost useless - given that building the first level takes around a day (unless you have Builder's Guild), every Governor will have gone from level 1 to level 2 the usual way. Then for each following level, the time it takes to upgrade it is similar to the time it takes a governor to level up again.

You are spending your time for nothing. Almost everything in this version is wrong, does not make sense or twisted. But nobody cares.