Which version of AWEB are you using? AWEB 3 APL is a bit more fault tolerant. The only other 68K browser I can suggest is iBrowse. I've not used the old 68K versions of voyager.
The most "up to date" (in terms of web standards) browser for m68k amigas is probably NetSurf, but I haven't tested it personally. I gather it is presently very slow.
If you want to browse amiga.org on your amiga, might I suggest trying the following link:
Amiga.org old browser proxy. This will rework it a bit so the lack of CSS and javascript is less of an issue.