There is an easy way to put an end to this.
Under FCC rules you are allowed to put up as many 1 Meter or less Dishes on your property to receive what you want.
The HOA guy hates Dishes of any kind - including D* and E*.
Inform him that to replace the 10 foot dish, you will be installing 20 1 Meter dishes all over your front area very close to the road. These will be needed to replace the 10 ft dish and legal under FCC law.
Let him know that once you do it there is no going back as the money will be spent. You might even take the photo you posted and photoshop in all the dishes so he can see exactly how it will look.
Ask is he sure that is what he wants or would he want to work out a compromise.
If he still wants to play hard ball, find the local D* or E* Contractor and get a bunch of old 18"-20" dishes they have replaced and start putting them up in your new "Dish Farm".
Unless they guy is a true idiot, he will decide 1 10ft Dish hidden is better than 20 1 Meter Dishes lining the Roadway for everyone to see.