I would be blaming Belkin.. you will find extending networks is commonly a manufacturer exclusive propriety setup.. the reason is simple.. the IEEE does not have a standard for WDS.. so it simply is a case of everyone did what was right in their own eyes.
Run ethernet to the Belkin.. if it doesn't have a WAP mode.. then use WAN BYPASS.
This is simple.. change the IP of the Belkin to the same as the Apple range.. but outside the dhcp scope.. eg.. TC at default is 10.0.1.1 and scope is 2-200
Set the Belkin IP to 10.0.1.222 (make it easy to remember as you need it).
Turn off the dhcp server in the belkin.
Save the settings and reboot it.. plug ethernet LAN port of the TC to LAN port of the Belkin bypassing the WAN.
On a computer simply go to 10.0.1.222 and setup wireless for roaming network.
Same SSID = Wireles Name.
Same Security.. WPA2 AES = WPA Personal
Same wireless password.
The only thing different is wireless channels.. and if auto does not sort it.. do it manually.. ie one router has channel 11 for 2.4ghz the other has 1.
One router has 36 for 5ghz and the other has 48.. or 150.. whatever.. something different enough they do not overlap.
If you run into issues just ask.