You can get meaningful improvement by getting a better amp regardless of the speakers you are using. The question is whether the improvement is worth the price. With speakers as good as the 30.1, I think that it would be worthwhile to spend a significant amount on an amp of your liking. I know many Harbeth fans like high power, but, I’ve heard, and liked these speakers with 50 or so watts of tube power. I think they sound good with less power than that, so I would look for quality, not necessarily quantity (I.e., watts).
I don’t know what $5,000 buys on the used market. I particularly liked these speakers with the Synthesis A100 amp and their A40 amp (both tube amps).