Me - I ain't smart.
Loose connections, in general, can cause heat. I suppose you could make sure the relay socket's female-terminals are nice and tight on the relay's male terminals. Are any wires also hotter than they should be?
Here's my thinkin: If anything in the circuit was overdrawing, the fusible link should blow before the relay or any wiring gets hot (whether the relay or pump or wiring cause the overdraw). Now as far as relays degrading internally, I won't pretend to know 1/2 as much as Tom, Joe, Saleen, et al - I'd leave it to one of them to comment about the contacts degrading, etc inside the relay.
In my experience, low voltage makes pumps get quieter. Now what does make them louder is cavitation. I cant think of a good reason why yours would though (you used a new intermediate hose that came with the new pump?). But that can make them loud and would obviously cause a stumble. And cavitation can cause the pump to start to fail (the diaphram uses fuel for lubrication and cooling - being deprived of that would shorten its life).
I know that really doesnt help. In a similar situation, I'd try your relay idea (I've been known to do a hotwire on a really failing pump, for diagnostic purposes - I sure
wouldnt one your nice machine though). And the pump and its plumbling inside the tank is what is left.
That be the best I gots.
Good luck with it brah.