I know these are not well received but I use a cheap cable box that provides nothing more than just access to channels. I think it would be a little better setup if I had something like an android tv over the top of it. Problem is it dosent look like anyone makes anything like that. Ive tried a cable card with an HD Homerun but Time Warner limits what you can use cable card for.
As much as I'd rather not suggest it due to the heresy of not supporting Android TV, have you looked into playstation vue? It's honestly the best option you have here for Cable Replacement. It's got a better lineup than Sling and it's not very expensive.
It's not an Android TV device, but have you considered getting an Xbox One? I don't know what you would like to do with HDMI passthrough, but I like using it on the Xbox One to watch/play one thing while I have my HDMI passthrough video snapped on the side.
Since you have a cable TV subscription, there are plenty of apps on the Xbox One that you can take advantage of.
You may try out https://www.sentab.com/kodi - it has an Android TV OS and supports HDMI-In/Out pass-through. Really convenient to switch between cable content and Android TV apps (Kodi, Plex etc) with no messing around with different TV inputs. Unlike some of the mentioned boxes from Chinese manufactures, it does have Android TV plus the pass-through works with cable box. Usually the chinese boxes does not come with hdcp encryption, which cuts off using them for set-top box pass-through feeds.
In the next year or so, I think we'll see all the major cable companies put out apps for popular streaming boxes that can take the place of simple cable boxes (and possible even cable DVRs). Time Warner Cable already offers such an app for Roku but unfortunately not Android TV yet. https://channelstore.roku.com/details/23048/time-warner-cable
There is always the Ziddo X9 or the Tronsmart Pavo M9, they both feature HDMI in. I've never used one so I'm uncertain if they can pass through in realtime, but something worth looking into that's much cheaper than an Xbox One.
I'm not sure that they run Android TV proper, but they do run a variant of Android.
Damn I've heard of the DRM for TWC. Have you looked into Sling TV?