For all practical purposes, HDMI is not "faster" than DVI in terms of performance. While some HMDI standards allow for more stuff to happen over the connection (audio, video, and networking, for that matter), it really isn't meaningful in this regard.
True, the digital signal is the same on the GPU side when considering whether to use DVI or HDMI, but on the monitor side it isn't. If you insist on using HDMI (I see no point in this), then you will have to adjust your monitor settings to meet your needs.
As recommended earlier, just go with the DVI connection.
Good luck!