I would suspect it is a matter of timing. With namecheap, I believe it does take a week or two for the whois data to become publicly visible. So I think it works in case you ordered privacy a bit later than the domain was registered, covering the data for the period of drop proceedings. And after that, the data will show it as not registered.
However, you seem to have bought the domains at the same time with the privacy service. So if it is very important for you to keep your anonymity, I would only extend the privacy service now, and not the domains. That might do the trick. With Namecheap it's around $7 per 5 names, so 80 domains goes for about $112, and once you et them drop, you can use the service on your remaining domains.
For the gap on protection of the other domains, just change their registrant info for the time being, by replacing your name with someone else's. Which makes it somewhat cumbersome. So maybe spending $112 is your best option?