My only choice is extending via wi-fi
Not sure why you say that.
If you cannot run the Ethernet cable, then you might want to look at Ethernet Over Powerline (EOP) adapters to send the Ethernet signal over the existing AC wiring in your home. The theory with these devices is that you already have the wiring in place, you just need the adapters.
A number of users have found that EOP adapters work very well...and they are almost always a better choice than wireless to try to extend a network.
Your local computer / electronics superstore will have a selection of EOP products, sometimes called HomePlug adapters. Tell the sales guy about the layout of your home, how far between AirPorts, etc and ask them to recommend the right product for you.
Just in case....also ask about the store's return policy.
If you don't want to try the EOP adapters, it would be a good investment to have an IT guy or lady come out and take some measurements to see if they have some ideas to improve things.
If you must connect AirPorts using wireless, about all that you can do is try to locate them as close together as possible and minimize the number of obstructions between them. Unfortunately, even a normal sheetrock wall can absorb 20-25% of the signal. If the signal has to go through more than a few walls, you really don't have much of a chance for reliable operation at all.
Within the last decade, a lot of newer wall insulation uses a metal foil backing on one or both sides of the material. It might be good for insulating, but it is a killer for a wireless signal.
As far as new products are concerned, my experience has always been that a new product will not solve a basic problem of poor signal quality caused by too many obstructions in the signal path. It couldn't hurt to try new AirPorts, if the store will let you return the products if things don't improve.
Good luck!