Chev unless I misread, what you're describing is a wired connection between the two. I don't have that luxury so I've got to setup a wireless client-bridged or repeater or somesuch mode. that is the way I had it in the past using dd-wrt wirless G devices. I need that sort of arrangement at full wireless N speed.
Just to get something talking, I setup the arrangement I think you're describing, with an old G router connecting wired lan-port-to-lan-port behind the newer N router and it worked, but reduced throughput anywhere/everywhere/every-connection to under 1mb/s..... not too swift. so that's unusable. there are a lot of moving parts here so the speed fault could be due to just firmware oddities or any number of factors, but that is not the ultimate setup. the right setup is a pair of "N"s happily sharing one wan [rr] connection to the world.
my search continues...
If you can't run a wire then you can use bridge mode which is like a wireless switch that you can plug into or you can set up a wireless repeater, although many repeaters also require a wire just like an A/P, the only difference being that the A/P can use it's own SSID, password and security rather than piggy backing the settings that the main router is using.
My point was that it's often times better to use a dedicated A/P/bridge or repeater rather than trying to make a router work like one. There is little doubt that using a dedicated access point is
the best way to create a wireless access point.
As for the wireless speed of my own access point, I get the full 300Mbps when using the 802.11n Only mode. Using WPA2 and AES encryption which is actually made to work with wireless N really helps to achieve the full potential of wireless N. my A/P is 20 feet across the yard from my wireless USB NIC.
So you can see that your experiment with old G or N routers has nothing to do with what is possible when using the correct hardware. I had no idea that you could not run an Ethernet cable which is the preferred way to set up an access point.
In your case it may be worth using what they call a wireless range extender, which is basically the same as a wireless repeater. There are lots of these around if you Google it.
It won't work as well as an A/P but will extend the range of your router without using a wire. You can see by the reviews that these do not work nearly as well as an access point would. Just depends on where you install it and the number of walls to contend with plus a few other factors. Good luck setting this up no matter what you decide to use. :)
Amped Wireless SR10000 High Power Wireless-N 600mW Smart Repeater
Amazon.com: D-Link DAP-1360 Wireless-N Range Extender: Electronics