Cloudflare APO for WordPress is compatible for WordPress MU, both with subdomains and subdirectories and really is very simple to use. Just download the plugin, log in to the account and activate APO (on all subdomains as well).
It costs 5USD/m.
https://www.cloudflare.com/pt-br/automatic-platform-optimization/wordpress/
Do I need to manually install it on each subdomain? This isn’t feasible for me because I have 100s of sites in the network
You just need to install the plugin on the website, login with your Cloudflare account and then activate the service via a button.
You must do this on each site you intend to activate the service on and the $5 per month is for one domain. If you have a WordPress Multisite you won’t have problems, but if you have multiple domains it will be 5$ each.
I was on the same quest as you and this was the best solution and the one that cost me time, money and headache, believe me.