Upon further consideration, I have thought of an indirect way one might go about implementing the UDP tunnel over HTTP. The success rate and reliability are unknown, but it is worth a try if a direct UDP tunnel cannot be established.
SSH is a TCP protocol. In theory, one could establish an SSH connection through the HTTP tunnel. A subsequent UDP connection could be routed through an SSH tunnel and the DAAP beacon relayed through that pipe.
Such a convoluted solution would represent a great deal of stacking and, given that you have indicated your DSL connection to be somewhat flaky as it is, may or may not be reliable. However, it may be worth a try.