I'm trying to understand what your dilemma is, but i'm having a hard time comprehending.. However, as someone who does maintenance, clean up, minor restoration, and who has and uses a Supra as well as Ludwig drums, i can only tell you that..
1- Sympathetic buzz is normal and can never be eliminated, whether you tighten or loosen your wires..
2- No amount of switching straps, cords, or snare strands will solve the problem you're having because if i've read correctly, you seem to be getting the same trouble with all your snares, which indicates the problem lies with how you set up your snare drums..
3- I have 4 classic Ludwig snare drums, of all different depths, shell construction, and hardware, some with original strands and cords, some with new ones all around, and i've never had the problem you seem to be describing..
4-I suggest you reassess everything you do when it comes to head tuning, tensioning, throw-off and butt plate adjustment, take apart at least one snare drum, and find a tutorial on Youtube on how to do all of what is required to get a good snare drum sound, and then compare it with the way you do it.. If there's a difference, then you'll know the problem is not your snare drum or it's hardware, but the way you personally adjust your drum..
5- This is just a suggestion, and is in no way implying that you don't know what you're doing.. This is just a personal observation, and i'm simply stating an opinion as to how to go about it..
6- When i started out, i had to figure out everything for myself through trial and error, sometimes with sheer frustration at the fact that for many years i was wrong at doing this or that, but 28 years later things are different..
Now that i know what i'm doing, I still find myself learning things, as i always have, even after 28 years of drumming..
I hope this helps you out in any way, and i would like to wish you good luck on getting your perfect snare drum sound.. :)