You are completely right. The function definition isn't included because I am not able to post them. For some reason it keeps timing out if I try to post or preview them. I'll try again later.

You are also right about the scalar function performance. Their performance is terrible and particularly in larger data sets. This was just an attempt to get the result first. Performance can later be improved by putting the functionality of the functions directly in the query.

I will wait to see if the OP can post some additional information that can help in solving this problem.