Yeah, I have the exact same issue with my 60's Slingy 12" tom mounted on the vintage rail. It also sounded severely choked and yes, I also discovered it's a common problem. Sure, one could use RIMS and this whole thing would be a non-issue but using RIMS on a vintage kit, in my opinion, looks hokey. Might be fine in the studio, though, where sound is everything.
Just curious ... how does your tom sound when mounted on the snare stand? I've also gone this route and have had mixed results. Some snare stands still choke the tom's sustain. I've had the best luck with an old WFL stand where there isn't really the option to tighten the basket around the tom. Using the WFL stand considerably reduces the choking but it's still not perfect.
I'd be curious to hear from others who mount their tom via snare stand. Anyone else have any choking issues using this method?