Hi Luke,
Let's try to get to the bottom of this. We'll need to get through some questions first.
Which label engine are you using? Maplex? Standard?
You mention that you can repro this on just two features - what type are they? points? lines? polygons?
Do you have label classes with SQL queries set up?
Do you have an advanced label expression that you're using? Is it querying out features to label differently?
How are you labeling the features? basic positioning? or are you getting into advanced fitting strategies and conflict detection?
Easiest thing would be to get me an mxd/data that shows the two features you're able to repro the slowdown with. That way I can easily compare the map in ArcMap and then in Pro.
thanks
Wendy