Serious signal degradation - should replace router with mesh network?

AT&T delivers 70 Mbs into the house where the wire comes into the wall. Signal degrades to 22 Mbs in the next room. and down to 1 Mbs in my office where I connect wirelessly.  Antique single story house with foot thick plaster walls seems to be the problem.

Cannot drill holes for Cat 5  - If I want to remain married  8-) 

Range extender seems to resolve issues for Direct TV on second box, but not for my office. 

Can I buy a mesh network setup such as Orbi or Eero?  These require replacing the router according to their adverts. 

Can I replace the AT&T router/

Should I?

Is there a better solution?