I visited the Museum of Orange Heritage at 386 Creagagh Road in Belfast in September 2016. This is their new center. The 1690 Account Book was on display under glass.
They have prepared an alphabetical surname index for the names that appear in the Account Book. I was able to check for my ancestors' names very quickly and easily. I did not find them.
I was told that the account book has 1400-1500 names which is far less than the supposed 30,000 soldiers in the army of William of Orange.
I arranged for my visit in advance by contacting the center through their Web site. It is my understanding that the Museum staff is willing to do look ups. I suggest contacting them through the Web site.
Michele