The radio engineering is all a mystery to me, but I do understand the astronomy. (I still think in terms of wavelength, not frequency!). It sounds like you're covering all the bases, though.

A few questions, have you considered rigging up some sort of equatorial clock drive or computer control on your altazimuth so your dish can track continuously and integrate on a spot on the celestial sphere? You could probably adapt one from a commercial amateur telescope controller.

Will your equipment automatically reject any modulated signal? I've always guessed that any ET beacon would probably have some very simple but unmistakeably artificial modulation, probably on a time scale of several seconds (a string of integers, the prime numbers, or just a rigidly varying pulse rate, that sort of thing) and repeated over a time scale of several minutes. My guess is any biological organism would probably have a time resolution capability in the second range, and minutes seem about right to integrate a signal so all the pulses would register. But we are guessing with ET.

You appear to be already exploiting earth rotation Doppler at your latitude and your target's declination to help characterize a signal, but have you considered also correcting for earth's motion around the sun as well? At 18+ miles per second, this could definitely Doppler your signals out of your band width altogether. This would also have to be further adjusted for ecliptic latitude of an object (signals approaching from the ecliptic poles would be unaffected, those from the ecliptic plane would be highly Dopplered). In addition, there would also be some Doppler modification of the frequency dependent on the angular distance of the target from the earth's direction of movement at the time of observation. Signals in front of us would be blue-shifted, behind us, red-shifted. Signals at right angles to earths instantaneous motion vector would be unaffected. It might even be worthwhile considering correcting for the sun's velocity relative to the Local Standard of Rest (the average rate of galactic rotation in the solar neighborhood).

We can assume ET, after picking an appropriate wavelength to transmit at, would adjust his transmisssion signal to compensate for his own motion and geometric effects, but of course, he would have no way of knowing ours.

Finally, have you tested your rig by attempting observations of natural radio emitters? These certainly could be used to simulate certain aspects of beacon signals to fine-tune your equipment and test your procedures.