Considering the HF bands (1-30MHz), as you get higher in frequency, less bending occurs for a given amount of F layer ionization and signals start to get lost to space. Shooting DX out 1200 miles will be difficult for you at any frequency when you are in a hole like that because the signals are hitting the ionosphere at high angle of incidence. That means you are sending everything above about 20MHz right into space and everything lower than 20MHz is making short ionospheric hops and will likely peter out before they get more than a hop or two away. Another problem is D-layer absorption on the lower frequencies which eats everything HF under about 10MHz during the day.
40m is good for daytime because it can get thru the D layer (hoping the F layer is strong enough that day) and 80m is good for at night where there is no D layer as the wavelength is long enough to bend in a weak F layer.
Look into something called MUF (maximum usable frequency) and a technique called NVIS. If you set up a good ground screen on the ground (rock is a horrible conductor) and a horizontal dipole just high enough not to zap anyone near the antenna (not much higher or it wont work), your signals will go mostly upward and you should be able to work a good 500 mile radius with a shorter hop, and perhaps the east coast on a second hop. As for reaching other countries from that canyon (outside those 3 directions you mentioned), ducting may be your only hope.
Grab one of the countless free pdf files online on RF Propagation. You'll need to know that stuff if you expect to pass your general and get on HF.
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