As a person looking to break into the product marketing space, what project experience, academic material or training courses would you recommend to build a relevant background?

^Agree. For more tactial tips: LinkedIn has some great overview courses on Product Marketing that is included with LI Premium. There are also local meetup.com groups that are worth checking out. Building a network and conducting informational interviews is always helpful and good practice for customer interviews you'll conduct as a PMM. For practice or even a makeshift "portfolio" you could take a current company and build out a fake GTM plan or updated messaging for the site. Presenting this in an interview with an explanation/reasoning behind your changes can show others how you think like a product marketer.

I want to see evidence of (1) strong and convincing writing ability, (2) excellent project leadership and (3) proven team-building skills. All of these talents should be demonstrated in a professional context.

I'd credit some school activities as relevant to product marketing: Did you run marketing activities for a professional club? Did you deliver an event from scratch? Generally though I wouldn't care much about academics or specific training. I have yet to see a school certification that is especially useful to product marketing.

Do plenty of networking---ask some of us on here for phone calls/coffees this holiday season.

You need to have strong writing and communication skills. A huge part of this job is communicating information across teams. In all product marketing roles, you will be evangelizing your product to sales teams. You need to clearly articulate the value of the solution you are marketing. The first have to convince sales that your product is worth pitching to customers. This true regardless of company size.