Given that the version of strip or appimagetool can cause build failure (I've experienced both and there are related issues 272, 299, 311) and it is presumably a challenge to find an optimal version that works in all cases, I suggest allowing command line parameters to be passed to the tool to allow using alternatives to the built in ones such as the system strip or a locally downloaded appimagetool AppImage.

It could look something like this:

./linuxdeploy-x86_64.AppImage \
    ...
    --strip /usr/bin/strip \
    --appimagetool /tmp/appimagetool-x86_64.AppImage