The high pressure pump does not throw it all up the top end and starve the crank, it has to go through the crank bearings on it's way to the top end!!
Unless you also add a restriction to the return flow/drain back from the head it will drain the same speed as before, more will drain though as there is more there to drain, if this were not the case it would all eventually be in the head, ie more is going up than coming back!!
HP pumps are normally used with higher rpm, or MUCH higher loads, a high capacity pump might be better, but either can cope perfectly with a external cooler, well slightly better actually as the oil will be colder thicker and easier to pump, maintaining better pressure.
A std pump will be fine at 350, and neither would cause inside leaks.
tabetha