After testing extensively I can confirm the following:
The PHP ini settings don’t matter. You can set the correct timezone in the WordPress settings, then set your airdrop times relative to that timezone. It should work no matter what.
If you have created your airdrop entry before setting the timezone, it’s best to create a new airdrop from scratch just to be on the safe side.
Also, if you are in a position to easily test on a different server, please do so.
This is again a case of “it works on my machine”. I am out of ideas right now, so I’d recommend that you set up an external cron to trigger your WordPress every few minutes. I will investigate your other requests regarding WCMp.