If you really suspect that toxic backlinks are causing your rankings to go down, then here's what I'd suggest:
1. Document all the suspicious backlinks that you've found.
2. If it's not a very long list, they're not your problem.
3. If it is a VERY long list, then put them on a URL somewhere.
4. Submit a concise Reconsideration Request disavowing any connection to those links, and include a link to that documentation URL you created.
I'd try this approach before twisting my site's URLs into some kind of knot.