Thanks for the replies.
I downloaded epiphany in cloud mode (booting from CD with the TC 5.0 ISO). Besides having a huge number of dependencies, epiphany was broken when I tried to run it. Error message was:
epiphany: symbol lookup error: /usr/local/lib/libgtk-3.so.0: undefined symbol: g_type_add_instance_private
Looks like a bad library, maybe because I was booting from an outdated ISO? I checked for extension updates but there weren't any.
Anyway, I think I'll stick with gtk2 apps for now, but revisit the issue if the apps start getting seriously outdated.
Thanks again for the help.