Does anyone have advice on how to start working in this space? I'm open to part-time consulting roles to start, with a long-term goal of contributing full-time to a forward-thinking Bitcoin company.
Obviously you can start with basically advertising yourself.
Starting here in forum, you can post about yourself and your services that you are willing to offer. That is if you want almost a freelancing job. But if you want to be contract-based and you want to work in a proper company then you should seek out companies who are related to crypto. I say good luck in all your endeavors!