You cannot run any persistent processes on your DH account, so running a Quake server or Tomcat would literally be impossible.
In consideration of that, I’m not entirely positive you can specify your own ports and such, as I’m quite certain DH would be blocking anything but those ports needed.
What you’re looking for is not shared hosting - but a VPS, partially-dedicated, or a dedicated server. I’m unaware of any shared hosts that’ll allow you to run your own server applications and such.
Chips N Cheese - Custom PHP installs and the like!