I didn't think I could do it when I saw the board but decided to try and turned out to be fairly easy. Here are the steps I took.
1- Removed the old batteries.
2- Made a cleaning paste using baking soda and water (google it, there are many sites that describe the method) and did a first pass cleaning, that got most of the buildup off the board. Let the board dry overnight over 1 of the furnace hot air vent or you can use your oven set at 175 degrees.
3- Did a second pass cleaning using isopropyl alcohol.
4- Then sprayed the entire board with QD electronic cleaner and that was it. The solder mask is gone but the board comes out really clean.

I found the most difficult part of the job was removing the old solder and the old battery pins and soldering the new batteries in but it was worth the effort.