You said: I think my next step will be to make a 3-turn helical coil tuned for 1686 and place it in a metal can wave guide.
I have never seen a helical inside any kind of waveguide but always mounted on a flat plate. The illumination angle of even a 3 or 4 turn helix is quite narrow and placing it in a can or waveguide even further restricts the illumination angle. Paul Wade, W1GHZ has written this up in his book chapter on helicals. I built some experimental helix feeds a couple of years ago and a couple of photos of one of them and its matching adjustment are View attachment 133096 View attachment 133097 View attachment 133098 attached.
What commercial sources do you know of that are selling 10', 12' (and larger) C-Band dishes other than the one in Ontario, Canada ?
Up until several years ago I worked at a satellite ground station (government contractor). I retro-fitted some legacy L-band feeds with helix elements for S-band. The dishes were .4 f/D with 130 degree 10dB edge taper. So, my research and testing resulted in a helix of 2.125 turns for optimal beamwidth. Two jobs later (did instrumenting of gun test for the past 5 years), I'm back in RF work (thankfully, as I started to miss it after not doing it for a couple years) and used these specs to fit a L-band feed on a 6' dish for GOES and POES satellites. GOES were kind of weak on the spectrum, but the LEO POES birds were booming.