Engine oil should not get to the transmission,
Quite the contrary in this case. On an Atomic-4 the "transmission" (more correctly called a "reversing gear" on an A-4) is more-or-less integral with the engine and gets its lubrication from the engines lubrication system.
and past the stuffing box (not on a working engine.
Shouldn't even get to
the stuffing box. With an A-4, there's an output flange on the back of the reversing gear. The prop shaft flange is coupled to that with four bolts. Obviously one should never see oil past the reversing gear case. (The foregoing assumes direct drive. I know not how V-drives are arranged.)
You should not
be getting oil in the bilge from leaving your shifter in neutral while sailing. You may tend to get a small amount
of oily residue in your engine space's bilge area, if from nothing else than blow-by. (All engines have some of that, and the original A-4s do not have a PCV [positive crankcase ventilationi] system to fully re-cycle crankcase blow-by). But that should result in no more than a slight
oily sheen atop your water in the bilge from time-to-time. And when I say "slight," I do mean slight
. As in: You have to look for it.
There are products out there you can place in your bilge that will soak up the oil and not the water. The most effective of these might be AbTech's Bilge Skimmer, based on their Smart Sponge technology. I have not found a place to buy that particular product and it's unclear to me whether it's re-usable. The other products claim they're re-usable.
(How the heck does one thoroughly clean an engine space on a sailboat, anyway? It's not as if one can climb in there with a power-washer. Least-wise not on a Pearson 30. Formula 409 and a boat-load of paper towels?
I recommend you carefully check your engine space for oil leaks. Get a nice, bright flashlight. For example: When I recently checked our reversing gear adjustment, I found that somebody, at some point, had failed to replace its case cover's gasket and that was resulting in a small amount of oil seeping out from under it. Wasn't enough to amount to an appreciable amount of oil in the bilge, but still: It's bad form
As for having that much water in your bilge after a few hours of your prop shaft turning while under sail: Sounds to me like your packing gland may need attention.
We put our shifter in reverse while under sail. But be careful: You probably have no neutral switch to prevent you from inadvertently starting the engine whilst in gear.