It doesn't seem necessary to get some big honking antenna on my roof.
If you can't do anything else, you might consider a really small antenna on your roof with an attenuator. Your root problem is that you have signals coming in at right angles to one another. For a single antenna you might consider a 2 bay UHF type pointed southwest. Example:
If that doesn't work you might consider two, perhaps more directional, antennas pointed at each cluster of transmitters and then combined.