I suspect your engineering effort is considerably higher than a civ SAR flight to produce that number of flying hours per day with an appropriately higher number of engineers.
Crab, you don't get it do you. It's perfectly feasible to maintain, and keep aircraft functioning at a high hourly rate per day without loads of engineers.
When do you need your max engineer strength? Not during the day, but at days end when the cabs are back in the shed. Balance your man power requirements, stop over servicing, keep them flying; when it stays in the shed something will break, put it out there and fly it, it'll keep turning and burning.
With 3 aircraft in China (One super puma and two pumas) we operated with 5 engineers, one electrician and helping hands from the drivers; meanwhile one engineer was always on leave. It can be done, but it needs organisation, co-operation from everybody, and speedy back up when a cab needs bits.
We are back into the circular argument about manning levels and the service's propensity to over engineer.
