By default, DansGuard listens for requests on port 8080 which is fine by me. I did not need to change the configuration of DansGuard at all.
Its import to run TinyProxy *first*.
With the two running, I was able to point to port 8080 as my proxy and lo! it all worked.
Note: For reasons I don't fathom, the speed problems I was witnessing with TinyProxy just went away. If anything, adding DansGuard would add an extra layer and thus exacerbate rather than amerliorate latencies right? Not so.
I've filed that one under problems-that-disappeared-in-a-disconforting-way.