It is always possible that the wiper relay is defective or the switch is dirty, but because you've got wiper position problems I'd look elsewhere first.

Likely the electrical contacts in the wiper motor gearbox are worn or out of adjustment. This often happens when removing the contact assembly at an angle rather than straight out (someone's recently been in there, right?). As I recall, the lower contact affects the intermittent wipe. Try carefully bending the lower contact up a bit.

There's also a small white plastic cam on top that opens and closes the contacts. This may need to be pulled and moved a notch or two to change the wiper park position. Once you've got the wipers properly stopping at the bottom of the sweep, you can then re-position the wiper arms to keep them from striking the window frame (wet window, high speed).

With a little patience and trial and error you should be able to restore wiper operation and alignment.