I don't know exactly how the engine chooses the files to autodownload. It downloads the pk3 of a certain map only when you have to play on that map... thus,
I suppose that it downloads the pk3 of a model only when in the server there is someone (a human or a bot) that is effectively using that model. I repeat, I suppose.
Maybe you may try to connect to that server (that you know holds that specific model) and use the /model comand to select it, even if you do not have it in your client: I have not idea if this will trigger the download process or not.About the slow download speed, the speed is limited to the \rate (client-side) and \sv_maxrate (server-side) values. Since the maximum, AFAIK, is 25000, it means that the maximum download speed is about 20-25 KB/s. To get higher download speeds, one has to use "www downloading", copying the needed files into an HTTP or FTP public web space, that will accessed by the client at much higher speeds. Take a look to
here.