My condolences. It is an absolute nightmare trying to find any documentation for dealing with time machine issues. I ran into that once and will never do it again if I can avoid it.

I have been super happy with CCC. I use it to back up my Macbooks to my NAS. Sometimes wired, sometimes wireless. And yes, it doesn't break when it gets interrupted. And their documentation is amazing. All the use cases and error cases are documented with solutions and everything.

I think I had two or three recoveries so far and have been happy with it. Even when it didn't work for some reason their documentation had workarounds.