Improve reliability of password manager for Epiphany 3.32

This is a smaller version of !214 (merged) without all the miscellaneous code improvements, so it should be suitable for GNOME 3.32. It includes just the reliability improvement and improved JS errors (which could be useful to have on this branch anyway, for bug reports if nothing else).

@jbrummer, if you approve, I'd like to try sneaking this in before 3.31.92 release tomorrow. :)