I have done some analysis about the period 2019-08-01 to 2020-03-31 which is summarized in [this CSV](https://gist.github.com/Glorfindel83/9de216d695b4fe737f2198c3c6f123d9). It is sorted by column 7, the number of views on Hot Network Questions per hour. [The Workplace](https://workplace.stackexchange.com/) is the clear winner here with 364 views per hour, having almost double the number of views of the runner-up, [Skeptics](https://skeptics.stackexchange.com/), with 188. Interpersonal Skills is number three in that list, so perhaps the unique configuration did help here, showcasing only the real gems on that site.

```
site				[-------BEFORE HNQ------]	[-------DURING HNQ------]	[Questions]	[Spots]
					views	duration	views	views	duration	views	#	%		#	%
										/hour						/hour
================================================================================================
workplace			898		09:27:00	84.7	10157	36:20:00	364.9	17	1.65	8	3.04
skeptics			444		09:52:00	34.3	11023	59:51:00	188.4	74	0.29	38	0.89
interpersonal		398		10:07:00	33.9	8388	52:40:00	153.2	87	0.19	49	0.50
movies				138		09:00:00	14.3	4728	33:09:00	140.2	46	0.64	34	1.05
parenting			325		10:17:00	14.7	7057	52:26:00	139.4	101	0.13	65	0.36
money				269		09:44:00	21.1	5215	37:25:00	124.2	30	1.15	14	2.18
academia			277		09:17:00	23.9	4960	38:51:00	121.1	15	1.83	4	3.62
softwareengineering	183		09:20:00	19.4	4119	34:24:00	112.1	62	0.39	44	0.69
security			283		09:41:00	15.9	5691	46:50:00	109.0	43	0.72	21	1.72
politics			252		09:32:00	22.1	4387	36:37:00	105.6	18	1.64	7	3.04
```

Some clarification about the columns: the average Hot Network Question on Workplace needs 9 hours and 27 minutes to become an HNQ, has 898 views in that period, which amounts to 84.7 views per hour. It spends (on average) 1.5 days in the HNQ and gets just over 10k views in that period. Not all of those views will be via the HNQ list, but if you subtract the views/hour from before the HNQ period, you'll get a decent estimate.

The last four columns are two ways of ranking all sites; by the number of distinct questions in the list, and the number of spots, i.e. how often the site occupies a place in the list. Of all Hot Network Questions in the network, 1.65% of those are Workplace questions, while if you pick a random Hot Network Question, it will be a Workplace question 3.04% of the time.

It's rather hard to say something about the least exposed sites; the list contains 156 entries, while there are about a dozen more sites which *could* appear in the HNQ but simply lacked the questions. Some of the sites who made the list had only one or two HNQs; not enough to perform a reliable analysis.

Data was gathered by downloading the Hot Network Question list every 3 minutes (similar to [here](https://meta.stackexchange.com/a/315017/295232)). The main difference is that every 15 minutes, additional data about the questions is retrieved as well via the [Stack Exchange API](https://api.stackexchange.com/docs/), including the number of views and the scores. Part of this data is loaded into a PostgreSQL database, of which a backup file is available [here](https://github.com/Glorfindel83/SE-Userscripts/tree/master/hnq-research); all data relevant for this analysis is in the `snapshots` table.

As for your last paragraph, those events aren't registered in this setup, but you might be able to fetch some of the data from SEDE, since it [records becoming an HNQ since March 2019](https://meta.stackexchange.com/a/324663/295232).