Question on keeping users on a particular server

Here is the background.  Have a web facing application - basic apache deployment web server front end, reporting and database server back end.  We want to load balance the front end and reporting servers for obvious scaling and redundancy reasons.  We have a pair of LM-2600's and they work as planned.  We have run into an application limitation where we need to keep users of the system from particular firms on the same web and reports server as we cache activity locally on the web server.  More detail:

Because it's a web facing app we can not control the source IP's.

We control user access across the product by unique user name.

We can read the user name value from an HTTP Trace:

I was hoping to build a content rule base on username that would be able to direct the connection to a particular server and keep them there for 24 hours.  I appreciate this will be a management nightmare to keep that rule set up to date but we have some programmatic ways to handle that.  Any ideas or anyone solved this another way I'm missing?

Thanks