This is an ongoing problem, although the behavior is somewhat different from prior builds. The severity and frequency appears worse than what I reported to Tablo Support in 2017.
When casting, if you switch to another recording, or tell the Tablo app to stop casting, the Tablo app aborts and loses control of the cast. The cast is not really gone, and you can see this by monitoring the cast with the Google Home app. The abandoned cast can still be controlled by the Google Home app, for example to pause, advance, or stop the cast.
However, the lingering cast prevents starting another cast of that same recording, or any other recording, without first restarting the Tablo app. But before restarting the app, manual cleanup is required. You can clean up the stranded cast using Google Home to stop the cast, or by casting the whole Android screen; which in both cases I suspect is best done when the Tablo app has been removed from the Android recent/running apps list available from the main Android screen.
Note: USE OF THE GOOGLE HOME APP THUS PROVIDES A VALUABLE WORKAROUND until the problem is fixed. After installing the Home app from Google Play, go to Home, then to Devices (click button at top right), then click the description under the image for that cast, which brings up the Google cast control panel. This allows you to pause, advance, or terminate the cast. This provides a way to deal with a runway cast, without having to clean up the cast and restart the Tablo app, which is very time-consuming.
The inability of Tablo to resume a cast without first aborting the app and performing cleanup is 100% repeatable behavior for Tablo with Chromecast; but is not a problem with other Android apps using Chromecast, such as Netflix and YouTube, which work as expected.
The Tablo app (or server) seems to be doing the wrong thing in the way it tries to stop a cast. The fix might be as simple as making a different call to the Chromecast API.
In a related situation, where the Tablo app spontaneously loses control of an ongoing cast, the Tablo app again cannot simply be restarted, because the cast is stranded. Although the cleanup procedures outlined above will clean up the cast, this shouldn't be necessary. When the app starts, it should clean up stranded casts.
There is also the problem of losing position within a recording, which can be frustrating when using Chromecast with Tablo, because when the Tablo app aborts, which it often does, it usually has not remembered the position.
The workaround is as follows. Whether casting or not, you can force Tablo to remember the position by pausing the recording, then leaving the player screen with the Android BACK button. In the case of stopping a cast, it is important first to not only pause, but also to leave the player screen; and then stop the cast. So when the app aborts, which it will when you stop the cast, the position is available after cleanup and restart.
Eventually, I think Tablo should frequently checkpoint the position, which would also cover case of spontaneous aborts of the Tablo app.
The Tablo logic for stopping a cast appears to be incorrect, and probably isn't hard to fix. The point here was not to solve all of the Tablo Chromecast problems, but instead to find a few that look easy to fix and would make Tablo usable without major inconvenience.
However, somewhere in the 2016/2017 timeframe, Tablo virtually stopped supporting Chromecast, and the top contributors in the Forum stopped responding to Tablo issues. At the moment, there is little or no evidence that Tablo is devoting resources to Chromecast.
Amazingly, reviews as late as 2017 still indicate Tablo supports Chromecast. https://www.techhive.com/article/3192442/streaming-hardware/tablo-review-a-complete-over-the-air-dvr-solution-with-just-a-few-flaws.html
In reality, we are left with Tablo Chromecast problems that are essentially deal-breakers, with no end in sight.
So I have concluded that it was a mistake when I purchased Tablo in March of 2015. I have started moving away from Tablo in favor of free or nearly free internet sources for most of my live or on-demand television program viewing. I can still use the antenna live to the TV for some programs, which has the advantage of dazzling quality for 1080i programs. I will leave the Tablo installed while I see how this all turns out.
cc- @theuser86 @snowcat @TabloTV @TabloSupport
Google Play services
version 11.9.75 (940-187402865)
System firmware version: 106401
Cast firmware version: 1.29.106401
Firmware for Tablo Devices:
Tablo Application: updated Jan 25
1.4.1 build 30004894 
Pixel1 and Pixel2 Android 8.1, Nexus7 Android 6.0.1 .
ubee DOCSIS 3.0 Compliant modem-router, Software Version: 9.40.1012, Hardware Version: 3.26.1 .