The tailpiece is probably not relevant to this problem, but you can fix the string alignment pretty easily by buying some new saddles without notches and having them fitted then notched in the right place to fix the alignment.
The alignment doesn't look too bad - strings go over the pickup screws nicely, so it's just the low E being to far from the edge of the fret board? High E looks pretty right (in the photo but could be different up close). Of course if you move the low E then the rest of the strings have to slightly move as well so the distances are all equal.
You could notch the new saddles yourself by doing it Gibson style - fit the new ones, line up the strings where you want them and then hit the strings down on the saddles with a mallet to make some notches! It does ruin that set of strings, and I wouldn't advise it! The job should be done with the correct files for your preferred string sizes. It can be fixed without major surgery. Not sure where you get the saddles though, as I assume they have metric adjustment screws and the easily available Gibson saddles for $20 probably wont fit.