Neither of those solutions work, exactly, because they assume too much about
how the data is structured. However, the idea of breaking the call number
down into multiple fields holds, I think, the key to the problem.

Incidentally, here's a description that's as good as any on how the LoC call
numbers are structured:
http://library.dts.edu/Pages/RM/Helps/lc_call.shtml

So what I'd like to do is break the data down into three columns. The first
column will have the initial 1-3 letters, the next will have the number
section, and the third will have the period and everything after. I'll
format columns 1 and 3 as text, and 2 as number, so I can tell Excel to sort
first by the first column, next by the second, and next by the third.

Now the challenge becomes, "How can I identify a variable number of letters
and copy them to the first column, and variable number of numbers after
letters and before a decimal point and move them to a second column, and the
decimal point and everything after into a third column?"

The third column ought to look like:
=RIGHT(B1,(LEN(B1)-SEARCH(.,B1,1)))

The first two are going to involve ISTEXT and ISNUMBER with IFs, I suspect,
but I'm less sure how to structure those. Thanks in advance for any advice
you can give!