Browser Support • Re: Pale Moon response speed under miserable ping times

my biggest fear is to run into somesort of a race condition where I start a new instance of the browser before the previous instance exited cleanly, and lose any of the permanent data storage I value so much

Pale Moon does guard against this by locking the profile. If you try to start on a profile that's marked "in use" it will give you an error message.

permanent data storage ... tabs

Keep in mind that open tabs are not necessarily "permanent". They are by their nature transient and unless you explicitly save them by e.g. bookmarking, sessions of open tabs can occasionally get lost.