Sounds like you want to be the guinea pig
You might try the WebDoctor first if it's just the phone app itself that is ill. I've never used it, but it might be able to tell you if something is fixable (instead of the hassle of getting a replacement Pre)?
So I'd say yes--basically what you're saying is correct. After the backup, on a new/fresh device root it, copy your backup onto the USB media drive, and then (after sudo'ing to root), do something like:
(ipkg install of gnutar first)
cd /
gnutar -zxvf /media/internal/bigbackup.tgz .
(X is extract, Z is gzip'ed, v is verbose output, and f is file.) The dot means to restore into the current directory.
And yes it is possible that some binaries will be in use when you try to restore them. In general this is not a problem in unix-land, but if you have a fresh Pre you're probably not concerned about the binaries, anyway--what you're really after is your settings.
It would be most excellent if someone with the webos emulator could try the backups/restores on a virtual Pre and post their results.
(Hmm...I think the backup command I listed above is missing the '=' sign for each exclude statement. Either I didn't type it in, or the forum software removed it for some reason.)