Unfortunately, it appears that I didn't get the right answer. Going back and rereading it (more carefully this time around), the desired date of New Years is:
1/1 if 1/1 is Mon-Fri OR Sat
1/2 if 1/1 is Sun
That's much more complicated. I found something that I thought would work...
1*1:0:1:0:0:0*NBD,BD1,IBD,FD1 = New Year's Day (Saturday)
1*1:0:1:0:0:0*NBD,BD1,NBD,FD2 = New Year's Day (Sunday observed Mon
1*1:0:1:0:0:0*IBD = New Year's Day (real)
but it is failing on some years. I actually think it might be a bug. I'll check into it tomorrow.
I have definitely decided that I need to add a couple more modifiers similar to IBD and NBD which will check if it is a given day of the week. That would make this much simpler. I hadn't been aware of the complexity of the holiday definition used here.