I'd chop the whole thing up and make a few plugs, making sure to free the roots of the plugs of their congestion, and start afresh, putting the container in the shade until the new plants establish. Your plan doesn't ease the root congestion that is limiting the plant, so it will only PARTIALLY reinvigorate the planting. Giving the roots to run will ensure full growth potential, within the limitations of other factors with the ability to limit growth, while potting up ensures limitations, the severity of which increases with increasing root congestion in the center of the soil mass. What you'll end up with is a perimeter of partially reinvigorated plants and a core of plants that exhibit little improvement from what you have now.

4 varieties of mint kept neat and under control by pruning:
{{gwi:43056}}

Al