What's your network software on the Classic? Have you tried setting up OpenTransport 1.1.x? With the Asante adapter it "should" act just as any 68k Mac with ethernet support, so there are (imho) no obvious reason it shouldn't work. I have never seen such an adapter, though.

I do network all my "without ethernet" Macs through LocalTalk Bridge with a serial cable connected to another beige Mac, and then via ethernet to my router, and it works like a charm.

I re-read the article you're linking to at jaghouse's, and I'm pretty sure the iMac he's talking about runs OS 9. Direct connection between a 7.5.3 and an Intel 10.5 machine just won't work.