Reddit mentions of THE CIMPLE CO

(Former cable tech here) Having Cat5/6 run as phone lines is really quite common in houses built in the past 5 years, and possibly earlier. A good thing to check on! Even Cat 3 can work, depending on how clean it is.

If you have drywall walls and an attic or unfinished basement running Cat6 isn't too tough (a good project to partner with a family or friend who is handy). You've tried the powerline/homeplug approach and know the drawbacks there. If you have coax already in place in the home there are ethernet-over-coax ways of networking (you can even use the DirecTV branded ones, such as https://www.amazon.com/Pack-Ethernet-Internet-Generation-Supplies/dp/B01N6YC9Q9). It is pretty plug-n-play, but like powerline devices will only give you signal if you have decent wiring (in this case coax) without too many devices or unused legs in between (splitters, etc).

In all cases when using existing wiring of any kind you will want to clean up the loop as much as possible. Ideally your wiring should go from one point to another without splitting or dovetailing to other locations. Check near your circuit breaker panel for a junction of wiring (both coax and telephone wiring usually comes into the house near there, often in a drop ceiling), and disconnect any wiring not going to your source and destination of traffic.