In a proper loop system, as long as circulation rate is sufficient, I would think the time coolant spends in the heat transfer stage is not important, since any heat transfer lost by rapid cycling is made up for by re-entering the cooling vessel more often. As an example, if short cycle time resulted in lower heat transfer, the engine would overheat at higher rpm and remain cool at idle.

Given an otherwise healthy system - including a free-flowing radiator - inadequate cooling is more likely the result of insufficient heat transfer surface area, insufficient coolant capacity or insufficient air flow to move heat away from the heat exchanger (radiator). Less likely, but possible, could be plugged engine cylinder water jackets.

Inadequate air flow can be the result of poor fan shroud design, bad fan clutch, incorrect fan cfm flow or inadequate fan speed.

Inadequate coolant flow at idle can be caused by a bad water pump or low engine idle speed, which if a mechanical engine fan is used, also reduces engine fan speed.

An electric fan should be ok at idle, unless the radiator fins are blocked, shroud design is improper, cfm is too low or low idle speed reduces voltage to the fan(s), causing a fan speed drop and cfm reduction.

I would try using the original shroud and fan with a good clutch and see if it corrects the problem..... but I'd also be thinking about a radiator with more capacity.

Frank