This feature appears to have either been quietly updated at some point, or not very obvious (or both!). But the ability to specify more custom date recurrences does exist!
Select the recurrence icon, then select the Repeats drop-down menu. The repeat frequency apparently dictates which customization options are shown. “Daily” and “Yearly” don’t have any modifiers; the rest are shown below:
Thanks @Adam_Caruso but this isn’t what we were looking for. We want to set something up to repeat on the 2nd Tuesday of the month, or the 3rd Friday of the month. These options (while great!) don’t provide that as far as I can tell.