I'd move...

. . .
cleg, I feel your pain... or I should say I've
felt your pain.
First, the streaming video on internet sites suck. I've tried to watch the preseason games that way for the past few years and I've gotten so frustrated that I ultimately just end up giving up. The feeds freeze all the time, the feeds are fuzzy and get knocked out quite often when the league finds them. It's such a constant battle with the sites that you just end up missing the game anyways.
A few years ago, I bought a single family home in a private and gated, deed restricted community. The HOA and board of directors are pretty strict when enforcing the declaration of covenants, conditions and restrictions. One such restriction, similar to the situation you're dealing with, is that a satellite dish cannot be mounted in which it can be seen from the street.
Well, when I moved in I was unaware of this restriction. When Direct TV came for the installation, I had them put the dish on the side of my house, as that was the best place recommended. Sure enough, a few weeks later, I started to receive warnings in the mail from the HOA to remove or relocate the dish.
My home faces south and the best location for the dish is on the west side of my house facing southwest. I had the installers come back to discuss alternative locations. There weren't any. The only other option was to put the dish on a pole in the middle of the yard... which would've been a worse location.
After some research, I subsequently found a Florida statute (can't remember which one now) that said homeowners have the right to mount a satellite dish for the purposes of watching TV. I presented this statute to the HOA and they bought it, but still said I had to move the dish. I invited the entire board over to my house and asked them to show me where it would be suitable, compliant with the HOA covenant, to mount my dish but to still be able to receive the signal from the southwest.
They ended up agreeing that there was no better location to mount the dish and I ended up winning my case with them. They backed off and I've been allowed to keep my dish on the side of my house, even though it can still be seen from the street.
I fought hard on this issue because I really dislike cable. Cable is not near as good, in my opinion, as satellite. Satellite has more HD channels, a far better quality picture, and of course, the Sunday Ticket. However, I have nine TV's in my house and it's not economical to have satellite hooked up to every TV, since you need a receiver for all TV's. So I get a basic cable package for the kids rooms and the pool/patio area and use satellite on the TV's in my bedroom and in the main living areas of the house. This works out pretty well for me.