Rodpad

Your other option is to gather shell out some serious cash for a better access point, or if you have a large house, a mesh network.

For such an old house, how confident are you in the reliability of the wiring? If the house had updated wiring within the last 1-2 decades, you can try Powerline adapters, but the speeds on these are unpredictable and dependent on the quality of the electrical wiring, etc. You won't know until you try it.
 
Since running ethernet doesn't seem to be an option, my recommendation would be to use a mesh WiFi solution. Personally, I prefer wired-in access points, but your situation/constraints seem to be ideal for a mesh system. The nice thing about mesh is that you can move the mesh points around until you get the best coverage and doesn't require wall/ceiling mounting; as long as it can be powered it's totally fine.
 
There are many mesh WiFi reviews online. Here's one from thewirecutter.com and techradar.com. I've heard good things about the Synology router/AP devices.

The listed access point has a better chance than anything then, as it has enough antennas to properly beam form (basically what occurs is the router uses the additional antennas to reflect the signal in the direction of your device increasing it's wall penetrating power) of course do expect some sort of degradation as the numbers like "AC5400" are merely theoretical, basically it's the combined throughput of all bands when hooked up via coax to a machine, as in real life you are dealing with the inverse square law, obstacles, and interference you will never achieve the listed speeds. (do note you will also want at least a  802.11ac wave 2 adapter to see close to the full connection speed on one device)