Check out 4nec2 first it is the Cadillac of free modeling software.
All the models you'll find on that digitalhome .ca site will be 4nec2 files.
Sorry to break it to you but a 7 foot dish still won't get you 20+ DBi @ channel 22.
I can maybe save you some time and effort here is a zip of the
parabolic models I used to compare 2 meter dishes and feeds.