I would recommend the RX100iv (even though it's just a little over 1k) not because I use Sony, but because of the high-praises, especially the ability to recover a decent amount of shadows with very little noise. This fits the bill for small, compact, video (even slow motion), high IQ, etc.

Of course, being only that it's a 1" sensor, there's definitely still limitations such as bokeh, ISO performance (though that's dependent on the user)
If you wanted, you could also get a good teleconverter and get double the range in an instant when needed if you need just a little bit of extra range.