... any advantage to inverted forks?
This be a can of worms I am not familiar with, but take it for what it's worth about front ends and what little I know. Look at that front end as if the bike could 'literally' hug the ceiling like a F1 car and the ground effectshit. I doubt they would swap the shocks upside down as if right side up would make a difference. Let that sink in as 'no advantage' you look at it that way.
... they will yield less unsprung weight...
I might be wrong on this but my take on 'unsprung' is anything under the spring? So the axle, wheel bearings, bearing seals, rim, tire, balance weight, air plug; is the unsprung part I assume?
but will also raise the CoG...
No, not if you think the CoG changed with the F1 car upside down, flipped the shocks upside down, etc. Make sense so far?
allow more or less flex at the wheel?
I would think the fork housing sleeve would be the same clearance for oil to slip in between is the fork tube. So upside down, right side up, same flex is at the sliding gap. Still make sense?
Do they provide a stronger mounting point at the triple tree/frame?
Once you lockup the axle at the bottom, the upper crown, and lower stem pinch bolts, that axle still flexed the same as if the shocks were flipped is no change.
I think the trend came from sport bikes.
Which came from motocross bikes?
Having the larger diameter tubes on top added strength where is was needed.
I have no clue, but to me, I expose less fork tube, flip the legs up the crowns; I chopped off weight. I kept the same leg length for travel, thus; Less fork tube needed = Pounds vs Stiffness?
Think about the torque lever arm under heavy braking for example.
I think I addressed that at the sleeve clearance is point Z. Flip the X or Y and Z is still the same under the same torque.
You can use the same argument for a chopper with the long fork tubes.
Here is where it becomes a 'dark art.' It's all about tire patch and how you angle the hinge.
I personally prefer the look of the larger tubes also.
I prefer to mess with the dials and springs and learn the art of the dark. Once 3-points are locked in, she is one moving unit. If I wanted to make it a plush ride, I'd cut some spring winds, toss in a cut tube as the preload height takes up those few winds, I could say I have an uncut #10 and a cutdown spring at say a 9.5 kind of spring rate. I add the 10, divide by 2 for a balanced rate set at 9.5 is the front end spring rate. Or, I could buy a #9.5 rated spring, have that full length spring in the fork; as an untampered #10 left original... that's the way they setup the high dollar front ends. Run #8's with a #10 and that says a balance of running a 9 front end setting: in the art of it.
The next deal are the compression and rebound screws. One fork leg only has a rebound adjustment, the other has the compression handled. Did not the factory look at the front end as one moving piece of balanced physics? So if I take the dark deeper, I could add that physics to a fork that has both comp and rebound in each fork and run all sorts of different settings off each fork and would it balance out?
Do the theories compute?