You talk of a 23,000 axle registerd at 21,000.
I’m guessing that your door jamb says 12,000 front and 21,000 rear.
And I’d guess you plate at 33,000 lbs.
I understand what you’re saying about the 12,000/13,200 axle.
If you want or need a 13,200 axle, just buy a 13,200 axle.
I’ve known people written up for being over 12,000 with 16 ply tires. It’s an inconvenience if you get written up. It can be a problem if you have to move or unload a few hundred lbs.
Few cops get that picky.
All it takes is one to ruin your day.