Sprockets have been available for belt drives for a very long time. Since Nexus and Alfine sprockets are interchangeable with SA (I'm assuming that Alfine 11 are the same as Alfine 8, the 8sp ones definitely are) it may be worth looking at prices for them as well if SA cost an arm, a leg and the skin off your butt.
I last looked at belt drive a very long time ago and in that historic era Gates advised against belt tensioners in any shape or form (more exactly they forbid them and any mention of them), the technology may have changed since.
I think the deal might have been change belt, change sprocket (soft alloy probably).
What's the bike?