In a regular setup like your current one, it is the AccessPoint web server that load balances requests to multiple QlikView servers. QVWS has this feature built-in.
However, when you use a desktop client with a qvp URL, you are directing your desktop client straight to a specific QVS, and gone is your load balancing opportunity.
However, there is a lower level-solution to this called Network Load Balancing. It's not software based, but utilizes a specific load-balancing network router. For some minimal specifics, consult the QlikView Server Reference Manual Chapter 17.
Got mail from Qlik and this is not something they support, but here's how it could be done.
""QV.exe is not able to use load balancing unless you use the Settings\User Preferences\Locations tab to configure the AccessPoint URL and then use the Tools\Open AccessPoint option there, then it can load balance, but what is going on in the backend is the AccessPoint pages are actually handling the load balancing at that point, whereas File\Open in Server is a direct QVP URL call to QVServer, and bypasses the web server/AccessPoint completely. "