Ok I can save like 400K by not starting the graphical launcher app that starts AmiTCP, but that's still not enough to get the web browser running

OOI which browser? NetSurf is available for some Amiga platforms IIRC

I was trying the version of Voyager I got in 1997, on the assumption that it's probably going to consume less RAM than anything that supports anything vaguely modern

Once online, I have ~1MB to run a browser