There is now the optional (still experimental) appimaged daemon that registers and unregisters AppImages with the system, including MIME types. If you’d like to try it out, head over to https://github.com/probonopd/AppImageKit/releases, and if it doesn’t exactly do what you think it should do, I’d be happy to hear about it on https://github.com/probonopd/AppImageKit/issues.
If everything goes as planned, this should give you the “open with…” option.