Hey @Lindsay,
Like you hinted at, this would unfortunately require some code customization. To get a basic sense of what’s required for modifying the default templates, I’d recommend first getting familiar with our “Themer’s Guide” here → https://theeventscalendar.com/knowledgebase/themers-guide/
That lays out the basic principles for modifying The Events Calendar’s templates.
With those principles in mind, you could then use tribe_get_events() under the month view to get the next event based on parameters you define. To get familiar with tribe_get_events(), you can check out this article here → https://theeventscalendar.com/knowledgebase/using-tribe_get_events/
I hope these resources help!
Cheers,
George