I've got IBrowse 1.22 (or is it 1.12?) almost running on my 2MB, Kickstart 3.1 A600 alongside AmiTCP. There are a few more memory-saving tricks that I haven't tried yet, though. The latest AWeb has been compiled for 68000 as well.
The patches to get IBrowse 1.0 up to 1.x were very difficult to find. As I recall, they were on an Amiga Format cover CD. I'll look again.
I'm not sure the picture datatypes are important - IBrowse has internal image decoders - but I had to turn off image loading altogether to save RAM.