How do you fix organic attribution of leads?

Product, growth and marketing folks, what’s the best way to implement some sort of tracking to sort attribution for organic leads?

Context - I head growth at a SaaS startup, with 40% monthly organic demos.

Problem - We want to be able to track our organic leads better to be able to put in more effort in the right channels. Other than trackable links and UTMs, overall it’s a headache to figure out where these leads are coming from. I know it’s not possible to fix it entirely, but any tips on how to make the attribution better?