While I can't answer your question, I do have a pair of the BD spurs. The entire system is very heavy duty in construction and extremely heavy. Frankly I think its overengineered for the intended purpose. Everything is attached via the very large and heavy replacement lugs. Be aware you will need a larger BD case to accommodate the system.

It doesn't answer your question, but I believe the rail is rectangular and slotted, so I doubt your arm is compatible.

You could use another atlas mount on the tom along with the Atlas Arch though.

I'm a fan of the Atlas mounts.

The Atlas Rail is round in cross section (although it isn't actually a tube) but appears to be larger than an original Ludwig rail. This still doesn't really answer your question because A: I don't know how the size of the vintage Ludwig rails might compare to your MIJ rail, and B: I don't know how much play your MIJ arm might have that might allow it to grip to the Atlas Rail. However my guess is that combination wouldn't work particularly well together unless you were really lucky.

The rail itself is tough to measure as it isn't a true tube but the Atlas Arch arm that rides it is designed to grip a 1" tube (I just tested that myself) so the Arch rail is 1/4" bigger than a vintage rail tube (which I believe were 3/4").

Since you can't generally buy the Arch without the upright (which works very well) you'll have it anyway I think you'd be better served to figure out a way to use it with your tom, probably the easiest thing being to either use a RIMS style mount or another Atlas bracket in place of a lug.

I use the Atlas Arch on one of my sets and it works quite well but the overall bulk of the thing is off-putting, especially with vintage drums. It does get the job done though.