Need Help Extending or Redoing Network in 3-Story Townhouse-- thoughts or ideas?

So I will start with the what I recommend as a last resort when your only option is no connection and therefore any connection even if it is poor is better than nothing.

That is a wireless repeater. You likely could place one on the second floor since you get good singnal and it would repeat it to the first floor. These devices have ethernet ports for your blue ray. Sound too good to be true and it is. You at a very minimum will lose 50% of your signal and they tend to be unstable and there are compatibility issues between some brands of routers and repeaters.

So real options.

Obviously ethernet cable with AP on the end to provide wireless is the best option. You could put AP on both the lower floors or only on floor 1 depends on where the cable can get.

The other are variations of the above replacing the ethernet with poweline as you mentioned. You can use 3 powerline Ie 1 on each floor and plug ap or switches into those and they will all communicate. Powerline tend to work very well or not at all, some houses they just refuse to work in because of the house wiring. All you can do it try it and return the units if it does not work

Another option that may work for you is MoCA. It sounds as though you have coax cable in most these areas. MoCa run network over coax. This generally works very well and is very stable. The risk you take is many of the cable tv and DVR manufactures use similar methods to do their whole house DVR solution. If you are very lucky they actually use MoCA compliant devices and you can leverage this to connect your equipment. BUT if they are not using MoCA you will just interfere with each other.

edit...
I forgot one other option. You can build your own wireless repeater that gets past some of the problems. What you do is get a device that act as a client-bridge (many routers can) and hook this back to back with a AP. You would use one set of radio channels to talk between the main router and the bridge and a second to talk to the end users on the first floor. This eliminates the 50% reduction because you have 2 real radios that can run at the same time. The only issue I would see is that if you run on 2.4g and wanted to use wide channels (ie 150m or higher) you cannot get 2 radio signals to fit. There is only 60mhz of bandwidth and the wide channels use 40mhz. You would have to move to the 5g band which of course has less coverage which is what you are trying to increase in the first place.