Ok, so we know ground is a problem, time to check the chassis grounds and fix that or you'll have electrical gremlins forever. Might as well do this first just in case it fixes the problem. I'm going to guess that the engine to firewall ground is bad or it is missing. Mine was not good, it goes from the driver side cylinder head to firewall. But I don't see why you couldn't run a ground from battery to the firewall. You are essentially doing that by grounding the wiper. The manual says that the wiper motor is grounded through the attachment bolt so I'd clean up that bolt and the motor and body where they bolt together.
I use this stuff on my grounds:
http://www.vetco.net/catalog/product_info.php?manufacturers_id=10&products_id=926
It's a conductive grease, it will protect the connections from rust and corrosion and helps with conductivity with uneven or pitted surfaces. It's the opposite of dielectric grease which is non-conductive so you don't want to use it where there are multiple connections in a single plug or you could have a short where you don't want it. I use it on my battery terminals too. Stuff is blacker than black from the carbon and will stain the crap out of whatever it touches (wear gloves).
Running only on high is the problem I had with mine, and two different techs said it was the wiper governor module.
When I pulled that out I saw that the insulation had rotted off and the wiring had rubbed through in a couple of spots. I taped it up and it worked again. Look for crusty connectors too, get some contact cleaner spray and wash down the connectors.
With intermittent wipers, high speed bypasses that governor circuit so it will work if the module goes bad.
For standard wipers it really is just the wiper switch, the wiring and the motor. Worst comes to worst you could wire in a standard switch, that was my fall back plan.
