This!! Exactly why I don't have engine bars anymore and plan to put the cooler where it's not adding frontal area.
I've been reading on air/oil vs coolant/oil. I do agree coolant/oil is superior. I may still go that way, finding technical data on this topic isn't the easiest thing, the Google machine generally returns nothing but anecdotal info.
It correlates heavily with PC water cooling, something I know well, but here's what I'm having a bit of a mental fix on.
Water based coolant has much better heat transfer than air over a given structure.
The greater the delta between coolant/air and oil the greater the delta before/after the oil cooler.
The question I'm trying to figure out is; is 100f air more effective a coolant than 180f water?
Secondary consideration is, I do ride it on the street, it's a street bike first and foremost, so that leans me towards coolant/oil, as you two gentlemen have suggested. Another very real consideration is placement and routing of the coolant hoses if using a coolant/oil cooler, there's no good way that springs to mind to plumb the system.