Interesting. I tried a different approach: no limits, except for normal daytime activities (e.g. normal sleep time). The result was what I wished for: eventually things stabilized. Yes, we went through several 2-3 day binges, when our kid would be completely immersed, but eventually she always got bored and seeked other activities (especially social & involving movement). After those extended screentime periods, devices would always get cast aside and used sparingly. So, it seems that at least some kids at some ages are able to maintain a reasonable balance all by themselves.
I don't know if this can hold (she's almost 6 now), but so far I'm very happy with the results.
I'm glad that strategy worked out for you. We might try it again at some point. But, evidence so far has shown that our children do not get of bored of playing on the IPad. At all. We could reduce the number of games available on the device, that might help. Also, the fact that the device has Netflix might be a part of the allure - when one digital activity becomes boring, they switch to another.
Thank you for you comment, I realize perhaps the device itself is not the problem but the number of available content.
Oh, I am not trying to imply that the same approach will work for everyone, in fact I suspect it will stop working for us once our child grows older. But I wanted to provide an interesting datapoint.
I don't know if this can hold (she's almost 6 now), but so far I'm very happy with the results.