Convergence in HFSS.
The number of converged passes setting is either in the solution setup dialogue or in the HFSS/solver settings. I don't have access/remember at the moment, but I'll verify which it is later. If you set the consecutive solved passes higher than the default of 1, often you'll get below .001 after a couple converged passes, but not always. Just depends on the problem. I always set it to at least 2.
Solution frequency sounds ok. It's all about electrical size of the entire problem, though, and HFSS may not be the most effective for this. Quick example:
I was doing a 14x14 microstrip patch array and we got some strange coupling in fabrication/prototyping, so we decided to simulate the entire array rather than use PBC/Master-slave. I had a PC with the same specs as yours and I was able to simulate the entire array using CST MWS, although it took a really long time. It was impossible to simulate the entire thing in HFSS due to the memory requirements for such a huge domain on my PC. HFSS just wasn't able to do this. We could've used a supercomputer setup to do it, though.
Also, how do you have the sweep set? Trying a fast sweep can kill the simulation if it requires too much memory, even when it actually finishes the solution at 10 GHz. If your PC can get through the initial simulation at 10 GHz, though, you can do a discrete step sweep and it should be able to handle that as long as you have enough hard drive space.