Near as I could determine when I was lookin' into it, the reported failures of internally geared hubs were all old, used & prolly neglected stock 3 speeds - there were some reports of new ones having problems, even the nuvinci, but those weren't on the SBP system with the lil 66cc china engine - they were on DIY jackshafts with much higher power engines... the lifans I think... I'd PM Pablo or Ghost0 to see what they recommend for an internally geared hub, they've been at it a while lol
As the chainrings are freewheeled on the pedal crank, a coaster brake won't work so with that in mind I purchased a Sturmey Archer S30 X-RD3 3-Speed Drum Brake Hub (bout $80) and had it laced to my original rim (heavier gauge spokes as well), it seems to be doing just fine
A disk brake in the front would be ideal, but fashion slave that I am I went with the Sturmey Archer X-FDD Dynamo Drum Brake Front hub, w/the built-in genny lights aren't a problem ('nother $80ish).
The Nuvinci is
a sweet way to go and I may get one if the Sturmey eventually fails me, but at $250-300, I've also looked into the Shimano Nexus Inter-8 Premium Hub SG-8R36 as an alternate for $100 less, both would need brakes ofc.
As for "the sound changed and it seemed to pick up power" I bet yer engine is finally broken in, what you described is pretty common and much sought after by new engine owners lol - I'd just check the plug's color and if all's well - ride on
Can ya post a pic of yer new project bike? We'd love to see it!