As someone else poking at an Actix-based hobby project, I get the impression that a lot of your troubles might have just been due to unfamiliarity with the architecture.
The solution to your problems with the Mailchimp crate was probably just to add whatever version of tokio your Actix is sitting on top of (cargo-tree helps here. 0.2 if you're on actix-web 3.3.2) to your Cargo.toml with the `blocking` feature enabled and then use `tokio::task::spawn_blocking` to invoke the sync API.
...as for Rocket requiring nightly, it's important to understand the philosophy behind it.
From the beginning, Rocket's been designed around "Make the most comfortable API we can and then wait for Rust to come to us", and they only recently started finding ways to dial it back a bit. The number of different API-unstable language features it relied on from nightly was a **massive** outlier.