There really isn't a known cure for dry mouth, especially since the medication you are taking is what is causing it. It would be easy if the medication wasn't necessary, but it is, so it's a side effect you're going to have to deal with.
Something I have always given my kids whenever they had a sore throat, dry mouth or fever was to give them popsicles to suck on through the day. It always seemed to help them and I even enjoy a good popsicle myself every once in awhile. It's very inexpensive to try and I think well worth trying just to get rid of that dry mouth taste. Italian ice cups are also a nice treat, but I'd stay away from ice cream products because of the dairy.