I'm going to put in the energy of meeting the person who did X thing, so I want to make the meeting count. 30mins isn't much time. What are some ways to efficiently frame my business such that I get advice / hear about their experiences that are most applicable to where we're at and which we can learn the most from? Just to clarify, I'm not looking to hire this person as 'consultant'; my question is really about approaching other founders who have done parallel things with their prior business.
After looking at your website, I would say clarify what it is that you do and more importantly the need you meet. As is currently, I have seen a lot of similar types of online companies and startups, not to mention the universities I graduated from send regular invites to video lecture series with top tier speakers. How do you not get lost in what is already out there? I also get feeds every day on linked in with these types of videos or events. It may be difficult to get the most out of your conversations without a more refined and differentiated product/service whereby you can pose your questions in light of your start up. It may be there, I just didn't see anything that popped and really stood out. And while it is rare, it is there. I have been getting pitch decks and proposals over the last few weeks and I was left thinking, "Am I being too harsh...is it me? Why does every stinking start up just blend with the next one that someone sends me?" And then I opened a pitch deck and it had that clarity, differentiation, to the point message...and it was like drinking crystal clear water. It may be in your startup...and if it is, I think you have to do a better job bringing it out on your website and from there..when you have your discussion you will likely get more refined and worthwhile advice. Just my subjective thoughts.
You should read every word they have written, grasp every concept they propound, and formulate a question about the most important fact or information they have published. You should memorize their complete bio starting from college and know what occurred at every step to their path to being an expert. Or, you could just treat them as a person with a story that may or may not actually impact your business. If you are looking for the perfect answer to the best defined question that will make all the difference to your business and path, you will be deeply disappointed.
If you feel as if you are having to "put in the energy of meeting the person who" [actually did something - an expert in your space], you should probably reconsider what you have done and go at it with a bit more respect. If their time is so precious that you are willing to ask it of the expert, perhaps you should also be willing to pay them their standard consulting fees, and provide them with specific questions you want to get answers to in advance. Then in the meeting (if your time is really precious it will be a call perhaps?) after you review their written answers, you can ask a few well thought out follow-up questions that call for a conversation.