Balancing Unbalanced Audio Inputs
The simplest way to balance an unbalanced signal is with an isolation transformer.  Unfortunately, a transformer that works well across the entire audio frequency range is going to be expensive ($>100 from Jensen).  

Another way to do it is to use a chip similar to the one you found from THAT Corp.  Is it overkill, probably.  But it'll be cheaper and perform better than a transformer (assuming that you don't really need the isolation that a transformer will give you).

The "typical" way would be to use two op-amps.  One is set as a mostly-unity gain non-inverting buffer and drives the + input of the amp.  The other opamp is set as a unity-gain inverting buffer and takes it's input from the other op-amp and drives the - input on the amp.  Vary the gain on the first op-amp if you need to.

Of course, the real question for this is:  do you need to use a balanced signal or can you get away with going unbalanced straight into the amp?  Of course, a balanced input will give you better audio quality but the op-amps or THAT chip will degrade quality.  If you don't do a good job, the net effect could be a decrease in quality.  And then you have to wonder if the change in quality (for good or bad) is even noticeable to your ears.  It's very likely that simply going unbalanced into the amp is going to be the better choice.