I want to ask for a significant salary bump from my next company as a freelance, do I need to provide verification about my pay?

You absolutely should. Freelancers of a high professional operational level would typically have very specific forms that show that they've been paid so much for their work. You have to compile these, show dates and demonstrate that you're worth that much.
I think a better way to negotiate what is basically a 33% raise, is to really show how much value you've brought to the startup. Talk to your boss about how things have changed for the work you've done and you'll have a better negotiating position.