The NetSurf browser the author tried out has multiple frontends. Two run on OpenBSD that I know of, the “default” GTK frontend and an SDL‐based framebuffer frontend. As was pointed out, GTK has a rather sizeable number of dependencies; building the framebuffer frontend instead would save a lot of time.
Mainline Dillo runs faster and smoother, it's just an fltk + git clone && configure +make install away.
(author) Is there a way to specifically build the framebuffer version from the ports tree? I didn't see one.