Too be honest, IDK, but I'm sure people are using them...aren't they?
I have a Shimano 9-speed, big deal. You said you were only using 3 or 4 gears out of seven, did you not? Why would you need seven if your only using 3 or 4 gears??? Just wondering bro, no need to take offense. And I realize gear ratios are of utmost importance....I don't know the ratios of any 3-speed internal hubs (because I've NEVER used them)and that's why I ask.
I like your set-up alot and it's far better than anything I'm running right now from what I'm reading here...like I said..."food for thought", maybe I missed a post on your trials and errors with a 3-speed hub and your prototype tranny.
That said, I'd be more than happy with a reliable 2-speed gearbox/tranny with decent low and high ratios, as opposed to a 7 or 9-speed derailleur system. And if you really want to get creative, ditch the chain and build a driveshaft.....cheers!