So here is what I have come up with.
I created a simple console application to point at the "Event" list and loop through each of the SPListItems in it. For each SPListItem, I output the fields and values. I then looked through the document and I found nothing that resembled the "Recurrence Display Text". I also looked at the Schema.xml and confirmed there was nothing in there that looked similar to what I was looking for.
I started dissecting other pieces. Ultimately what I found where two controls:
I opened these up with Reflector and analyzed the internals.
RecurrenceDataControl appears to be strictly for EDITING recurrence data. Nice because this saves me from having to write this UI myself in my custom form. I can just instantiate an instance of this control and pass it a reference to the "RecurrenceData" xml (and give it references to item/list/web context).
RecurrenceField can be used for either EDITING or DISPLAYING of recurrence data. This is controlled by the ControlMode proeprty. The difference between RecurrenceField and RecurrenceDataControl for EDITING seems to be that RecurrenceDataControl only handles the xml portion of the recurrence data (the "RecurrenceData" field in the SPListItem), whereas the RecurrenceField control appears facilitate the checkbox/toggling functionality (and corresponds to the "fRecurrence" SPListItem field).
Simplified: RecurrenceField uses RecurrenceDataControl.
For getting at the textual representation, then, I can use the RecurrenceField control. The problem is, I need just the text, no markup. I don't actually want to let this render down myself (ultimately I am returning this text through a service layer). I am accomplishing this by the following:
StringBuilder sb = new StringBuilder();
StringWriter sw = new StringWriter(sb);
HtmlTextWriter htw = new HtmlTextWriter(sw);
RecurrenceField local = new RecurrenceField();
local.ID = "testing1";
local.ListId = List.ID;
local.ItemId = Item.ID;
local.FieldName = "fRecurrence";
SPContext context = SPContext.GetContext(this.Context, Item.ID, List.ID, Web);
local.ItemContext = context;
//local.RenderContext = context;
local.RenderControl(htw); //this is the KEY!