After more talking and some thinking I have more things. Sorry this thread is kind of like a place for us (me) to brainstorm; as always, if there are other ideas out there I'm certainly interested in hearing them.
So other than a few minor technical things (like Goko letting me start a game of Dominion, no bigs) I can probably start streaming when I just play matches. It's not too prohibitive at the moment, and it should become much less prohibitive when I upgrade my computer, which should happen shortly. I think I have a decent idea for what direction I should go in terms of content, so thanks to everyone who has responded here, that helps a lot.
It seems that the main challenge left for the future of streaming Dominion is building an audience. It's probably the case that these other games are bigger than Dominion so it's easy to just start streaming them. Nobody is out there wanting to watch Dominion streams because nobody is streaming, and vice versa, so if this is ever going to get off the ground, someone has to break the vicious cycle and that's probably going to take some effort.
Well I'm not exactly the kind of person that's going to let the reason why this doesn't work be because I didn't try.
So I'm at least going to put in the effort; and the obvious starting point is the community "here". ("here" means the people who read the forums and the people who watch on YouTube) I can plug my stream here and on my channel, and other people here can either watch it and/or recommend it, and I feel like if it's going to work that's our best chance. It was also recommended that I have a schedule, where I at least stream at a certain time every week. Once there's an actual audience, it's going to be much easier to expand that audience.
But that doesn't happen without support. If I don't get it, that's fine, I'm not offended, but I'm at least going to try and do it. So I think I'll try doing a stream once or twice in the next couple of days and see if anyone wants to watch, and see what general interest is. Maybe it will take off, who knows?