To see what your settings are hold down on the Info button 5 seconds scroll down to view information.
The R22 is locked to be an SDDVR.
Native is shown as Off in the Info page. I doubt changing the aspect ratio would do anything, but I could always give it a try. That's really the only thing I can change in the HDTV section.
Sorry, I didn't realize that but it sounds like it's time for an upgrade. Appears you have an HDTV but a SD DVR. I understand that not everyone wants HD and the fees that go with it.
You were right about not seeing any difference with HDMI cable. It wouldn't hurt to go back to your other cable (I thought Component cable was included with R22; makes no difference anyway; your box is capable of displaying 480p but HD channels are locked out so I don't think there's anything to gain unless you can tell the difference.
At least you can get your channels switching faster with your old cable.
As far as upgrade lease and HD access, call DirecTv and see what they can offer. CSR's can extend some credits to offset initial upgrade lease fee for 12 months but it would depend on your account status, standing, and your individual circumstances.