No seriously, like 18 months ago I solved this exact issue in my corner of the world by simply creating a static website and putting them there on a calendar and now I'm like a microcelebrity of my own running a "brand" that every organiser knows of.
What makes you think that? Google/chatbots need a crawlable source. Instagram content is not a crawlable source. Be that crawlable source and they'll send the traffic your way. I get thousands of monthly visitors from Google alone. The next step in the funnel is to make them sign up for a weekly newsletter.
I'd also suggest a giant "purchase ticket here" button on every event page and measuring how many people click on it, it's infinitely easier to approach the organisers when you can easily whip out that statistic on your phone.
Additionally, an "MVP" could be a single HTML page, which lists all the recurring events, grouped by week-dat on a week calendar. For example, if there's a venue which hosts a weekly jam session on Thursdays, you could add that once and it would always show up for the "What's happening Thursday?" area. Usually there are a bunch of recurring events in any town, so the calendar page quickly becomes a useful "what to do today/tomorrow" guide, with minimal effort.
You could do something similar and then print out physical copies of it and hand over a few to local music venues, cafes, pubs etc to spread the word.
Fuck instagram.