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I've got a lawn boy 10684 that is leaking oil profusely.
I've disassembled it to some extend. The Breather on the top of the engine seems relatively dry, so does the top seal.
The oil seems to be dripping from underneath the head. Any common leaks in this area?
I've never taken a head off of a mower, and I don't even know how these mowers work particularly, but it almost seems as though the leak is coming from where the head meets the block?
I grabbed a picture off google and used red to where I think the oil is coming from (very poor drawing, lol) and green where the oil is pooling/running.

There is a cover above the red in your picture behind the intake manifold that is called the valve or breather cover. it could be leaking from there and then running other places. Also other possible location could be the sump gasket around the oil pan leaking which can cause almost the same effect. You could try cleaning off the oil really well and then run the mower to see where it is coming from.

Could I remove the valve cover and replace the gasket, or use rtv similarly to on a vehicle?
I did manage to presssure wash the mower, but still struggled to pinpoint the leak.
It doesn't leak while it's off. Doesn't leak when I first start it up, but after running for a few minutes it comes like a flood.

The very first thing I do to find a oil leak is clean everything real good. Then take a brite light and start looking. Might take more then one try but it will show up.