As a rule of thumb I normally suggest to avoid using routers as wireless clients; most of them do not support it anyway. The good news is the WRT54G makes an exception to this rule with third party firmware installed. I have found
DD-WRT works very well when configuring one of these in client mode, and it also means your main access point (or router) does not need to support WDS.
Unfortunately the WRT54GC is based on totally different hardware and does not support modified firmware, although it should make a good replacement for the D-Link.
Is your Airport Extreme is configured as a wireless client for the stereo? If that is working then there's probably no need to change it.
With regards to the range issue, if the signal is good from upstairs but access is slow then I'd suspect either the device you used reported its reception incorrectly (sadly not uncommon!) or there is some interference, perhaps from a cordless phone or neigbours WLAN. Changing the channel of the main access point/router may help if the latter is the case.