I was inferring (bad stinkie, BAD! No inferences!)from your post that the VX rim was 9.x lbs and the steel were one lb heavier each, and there being 4 wheels on the car, times a factor of 7 for sprung vs unsprung mass, got (1lb)X(4 wheels)X(7:1)= 28. Now I finished reading your calculations by paying attention to the details like his fuel mileage, the EPA's guesstimate on weight's impact on FE, and the final FE increase calculation of .5%. I see you said they're 4 lbs heavier each. Missed that. Sorry.
All things being equal, light rims/tire combos will return better FE than heavier combos. And at even 2% better FE, how many gajillion miles will need to be driven to recoup the $240 price (plus skins)? And does that even figure into the equation if he's a "hypermiler at any cost" kind of guy?
I usually pay attention to the details, they're alarmingly important. Details kept me from filling my deer tag with an Irish Wolfhound some years back. It was the correct size and shape for a Virginia Whitetail, but the lack of antlers and odd gait made me believe it wasn't a deer. I am truly glad I didn't harvest it; I have never enjoyed the taste.
More importantly, I think the guy just got some new rims, and if you tell him to be careful and easy on the gas pedal, watch yer speed, he'll do it and realize some pretty good numbers. Just cuz it's a placebo doesn't mean you don't feel better. Ya gotta watch yer brains, they'll mess with ya. They're always there, always thinking, whether you know it or not.
the cost of the rims can be offset by the cost of tires that fit them, the tire for 17" rims that I found in a 20 second search ranged from $73 up to $145, where 13" rim tires range in price from $26 up to $45, so right there the rims can pay for them self.
I agree on the unsprung weight, less is better, there is simply no way around it, I notice when I switch to steel rims with snow tires even tho it's only a few pounds per wheel, so droping from 17" to light weight 13" rims should make your car handle alot better if nothing else.