Hahah, well that's comforting to know I'm not the only one lost by this!
Definitely looks like I'm using 1.19.0; my package.json and the package.json of the gsap folder in my node_modules folder declare it as 1.19.0
Definitely have both babel and webpack; The rest of my ES6 stuff seems to be working fine.
So while writing this message, I managed to crack the issue! I started creating a test project using a stripped down version of my existing project, and suddenly the errors all went away. Upon closer inspection, it turned out that I had been a giant idiot, and I actually still had the cdn links in my footer from when I was prototyping the animations last week.
Apologies for the time wasted, hopefully this information saves someone else from an impromptu trip the the barbers!
Just for the record as well, I still found that if you import { moduleName } from 'gsap', you don't actually make any filesize savings compared to importing each module individually.