Well, I dug a little deeper into my Wii Shop issues. Lately, I've only been able to get on in the early morning, despite no trouble with any of the Wii's other online services. So today I tried in the evening again, figuring that since it wasn't Monday, I might have some luck. Nope.
I read through all of Nintendo's online help stuff for setting up the Wii online and tried two things: changing my router's mode and its broadcast channel. Now, I don't think there'd be any interference since I don't have any cordless phones or anything, but changing the mode from B Only to Mixed seems to have had an impact. I originally had it set to B Only because I wanted the DS to get as clean a signal as possible, but I guess that wasn't necessary.
On Mixed, for whatever reason, I can now get into the Shop. Now, the true test will be on Monday when traffic is heavier, but it's interesting. It's not like G is that much faster than B, especially since both protocols transmit data faster locally than what I'm getting over the cable line anyway. I have noticed that the Internet and News Channels run faster now, but they worked pretty well on B Only too. Now I'm wondering if Nintendo has set up the shop to give logon priority based on lag or something. Hmmm.
Also, just for the record, the Wii can't get on the internet at all in G Only mode, though it does recognize the Access Point (this is a documented issue on Nintendo's site, but it's not clear if it's universal or only affects certain routers).