All depends on Your definition of "performance". If it's "the best water resistance with the best vapour permeability and lowest weight", I'm afraid You'll always end up with something with Gore logo on it.
That being said, anything You're willing to compromise on brings You closer to the goal of having a natural fiber outdoor hard shell.
Personally, I'm currently experimenting with waxed fabrics. Commercially it's made by plenty of outfits like Fjallraven and Barbour, but the basic idea is pretty simple - take any mechanically resistant fabric You like (cotton, linnen, hemp, whatever blend seems like it could resist about 70 deg. Celsius), apply a wax (usually some mix of beeswax, parafin or microcrystalline wax, sometimes thinned with oils and solvents) and heat the whole thing (either with a hair dryer, heat gun or throw in a bag in a dryer).
The result is usually somewhat heavy, but surprisingly resistant and depending on what materials You start with, can be pretty cost effective.
I think for a rain jacket you have to compromise on the performance. It'll be a bit heavier, maybe just water-resistent and not waterproof, and likely expensive.
