Cool, thanks for all the help guys. I mounted it closer to the resonant side, like Snare Tan's picture. The name badge was loose enough that I was able to flip it 180 degrees, so now it's right-side up. The badge isn't loose and doesn't rattle, but was still able to be (barely) moved, which was good.
Snare Tan and billnvick bring up good points. My rack tom is an 8" x 12" and is the only rack tom with the kit. In playing position with the tom mounted on the left side of the bass drum (with 12 o' clock being the furthest away from me and 6 o' clock being the closest to me), the name badge is at about 9 o'clock. Kind of strange, since we know that very few MIJ kits from that era came with anything smaller than a 12".
Incidentally, I do not have a rail/consolette mount on this bass drum. Mine is a single post with a dual clip mount holder (similar to a Grestch round badge double tom holder). The clip "arms" are independantly angle adjustable on one center post. So I guess I could have mounted this closer to the batter and not had the rail problem to worry about, but I still like it better towards the resonant side. Thanks again for all the information!
It's funny, but with the clip mount towards one end of the tom, that's about the same place where Yamaha places their YESS mounting bracket, because that area of the drum is least effected by it. Maybe these MIJ companies were smarter than we thought?
I don't mind the clip style mounts. They are the only mounts that I haven't wanted to use a suspension mount on...they actually don't hinder too much resonance from the drum at all. Plus the lugs stick out further than the bracket does, so it's super easy to get into a case, or to get two mounted toms very close together.