I had contacted both iControlWP and BlogVault (as already mentioned), that both allow such site management (plugin updates, etc.) from a central place.
For the time being, no commitment from iControlWP, mainly due to additional workload it would mean and uncertainties about the prospects of CP; in case, CP gains a strong following and iControlWP gets a number of requests, I understand that it might be considered.
As already mentioned in another thread, BlogVault promises to support ClassicPres. And they seem serious about it. See the attached screenshot of my BlogVault panel: the site on the top has been switched to CP. In the listing, it shows as being on WP 4.9.9, but not in need of update. The site below (as well as the other ones) are still on WP: they are listed as being on WP 4.9.9, but in need of update (yellow), which shows that BlogVault recognizes the CP site as different.
I have written to support suggesting that CP sites might be listed as such, instead of being shown as WP 4.9.9 - but I could understand that they would prefer to wait until the stable v. 1 is out.
The real test will be if the core icon will turn yellow at the time CP updates come.
I would say that such management tools have saved me many hours of work, and allowed to keep an overview on the status of some fifteen sites. Definitely, I could no longer see myself working without them in the long-run. Not even mentioning the safety provided by those external, easily restorable backups.