The carburetor should (must) be located in an area of higher pressure.

The air inlet on the cowling of an airplane should be 0.35 * HP = 0.35 * 160 = 56 sq-ft. (total of both sides). The helicopter will have a slower forward velocity and the gearbox will restrict the airflow, therefore the inlets will have to be larger. Offsetting this slightly might be the fact that the aerodynamic rotorhub may 'scoop' some additional air into the inlet duct.

Perhaps give the engine compartment inlets in front of the two banks of cylinder heads and have the free-air flow between the rotorhubs and the top of the fuselage to pass on through into the upper quadrant of the propeller.

Locate the outlet duct somewhat above the propeller's axis of rotation. This may place it in a region of lower pressure, which will increase the airflow through the engine compartment during cruise. It should also improve the distribution of the free-air flow to the quadrants of the propeller.

The oil cooler will probably be located in the airflow near or just after the middle reduction. Its dimensions will be approximately 7.75"L * 3.5"D x 4.75"H. See Spruce, Wicks etc.

A question. ~ If the air is being withdrawn for the engine compartment, ie. if the engine is in low pressure, would a slightly larger oil cooler compensate for the reduced air cooling on the cylinder fins?

Ducted cooling fan: Consider mounting a vane blower on the propeller shaft, just inside the sheave. The cowling will end as a ring, around the starter ring gear, but with a 2" larger diameter. The vanes will have span of 2" and their root will start at the OD of the starter ring gear. The blower rotates with the sheave. In other words, the prop and the blower are rotating at all times but the prop only provides thrust when its variable pitch is directed to.

The incoming air to the blower comes from two 'scoops' which are located just below the secondary reductions on both sides of the pilots head. Additional air might come from the top, just aft of the two rotorheads. This might reduced the drag around the blade roots and the fuselage, provide a little additional lift and decrease the forward 'draw' of the two forward facing openings.

Most of this air would flow past the engine and some past the oil cooler. It is then exited rearward by the blower. The volume of air is sufficient for cooling during hover. During fast forward flight the airflow entering and exiting the 'engine compartment' will be greater and might reduce the power consumed by the blower.

A disadvantage is that the air density in the engine compartment will be lower than if the blower was before the engine

The radiator ......

Consider locating the fan on the shaft between the soft start and the mid reduction. There could also be flaps in parallel with the fan and when the forward speed is generating more volume than the fan is moving the flaps will open up.

The pressurized chamber must be leak proof.

Consider carbon baffling, as used on Zanzottera. Can withstand heat? Fewer parts than the conventional baffling for Lycoming. Can be contoured better for the requirement.

Consider an electrical fan for additional cooling of the engine oil.