MST3k typically had 24 episodes a season, and part of the shtick of the series was that it was a relatively cheap production with a small crew licensing movies that cost almost nothing to show.
I get that we're motivating folks to gather together later in their career than before, and 'competing' with other opportunities they have - but if you're going to start up the engine, seems a bit of a shame to pre-plan to shut production down after 12 episodes.
Heck, given the nature of the series, you should really be mixing crowdfunding sources a little. Yes, the Kickstarter is important - but you should connect your stretchgoals to Patreon income also, and permit a couple extra options.
1) After the "pre-funded" Kickstarter episodes, let Patreon income build up funds for future episodes - while still keeping a nice mid-season break and even cast shifts as needed for quality of life.
2) Let the show grow as you go - keep your megacheap ethos/comedy style - but if you find a nice line of comedy, you want to do a special on, let it get a sub-fund and decide how it can fit into the schedule. 100,000 patreon fans contributing 1-10 bucks can get you more than enough when you've already got the set and many other things. That, and likely chances to get secondary income streams.
3) You know you're VERY likely not going to get a really good deal with a cable channel. Don't let the shiny prize of a commercial-pushing income source let you shortchange your audience on things like DRM. Do it for you too - make a show you'd like to make first, compromise where it matters least as you can, and the audience can do more than the promises of any executive. Let us circulate the '.mkv's.
4) Stay cheap, the audience will help. Don't do silly things like commission CGI movies of fantastical comedy scenes as part of your budget. Ask the audience to help, and we will make the stupidest, most hilarious things for you. Use that - USE IT!