Jan,
I'm going to (in as friendly way as possible) disagree with the "air-pocket" hypothesis. Here's why:
Air pockets generally form in a closed system. If the system is open to atmosphere on the low side, and the pump is strong enough, it will push fluid through all of the piping and attendant what-nots on the "high-side" of the system. Any air in the system will be pushed along by the wall of fluid pressure building up behind it, because it has a place to escape to.
In a hydronic system, air-pockets form because the loop is closed and trapped air has nowhere to be vented. The air almost always moves to the "low side" of the system when they do air-lock. We put air-vents everywhere, but there's seldom air in the "high-side" of the system. The oil coolers are all part of the high-side-- taking 100% of the oil from the oil-pump.
The oil-pump itself is high-pressure/high-volume and self-priming. The suction side of it is at or near 0 psi, and always immersed in oil. The entire engine is an "open system" (is vented to atmosphere on the low side, which is the crankcase), so the thought that the "radiator-style" oil cooler would vapor-lock with a pump as big as a standard oil-pump is almost impossible.
In order for what you are saying to be a problem, the oil-pump capacity would have to be really, really tiny. It's not. That pump moves a lot of fluid, and is capable of generating a LOT of "head-pressure". With thick oil, it will generate enough pressure to explode a standard oil filter, and enough volume to empty the crankcase in seconds.
Anyhow, the "radiator style" micro-channels (the passageways between the "tanks") are pretty small. The oil-pump is going to fill the supply side of the radiator (cooler) first, because the oil-pump has way more capacity than the bottom couple of rows of channels. Once the tanks fills, the pump is going to push through all of the channels, fill the other tank (on the outlet side of the cooler), and then push through the galleys. There has to be a pressure drop across the sides of the cooler, but I'd bet it's small enough to be insignificant.
If the pump was lazy enough to not be filling the oil cooler, then the galleys would be seeing 0 psi of oil pressure. The fact that they see 40 psi+ tells me that the oil cooler is full.
As far as putting the fittings on the top-- I can see that there would be some advantage to that. The cooler could not drain down in the off-cycle (when the engine is not running), so it would remain full and able to supply oil to the galleys almost instantly on start-up. The disadvantage would be that the cooler would always be full of oil, and to do an oil change would require removing it and turning it upside down to get the oil out.
At least 75% of the people running oil coolers use the "radiator style" EMPI "Mesa"-style coolers. I'd be 95%+ have them mounted with the fittings down. They all work.