TOPIC:

You can fit a plug so 100% of the oil flow goes through the cooler but personally I would want to increase the port size (as injected has done with AN fittings) to ensure adequate flow

What Injected did works for aftermarket radiators.  But I'm using factory and the port ID corresponds to oil line ID.  To change volume through the oil cooler would mean to change the entire system with something that has larger lines, and core piping.  Regarding oil flow, I'd like to remind that there is a diameter reducer - oil jet - at the base of the cylinder and also an oil jet between the top of the cylinder and head.  Both of those jets are much, much smaller and increase overall pressure in the head.

I assume you have the Zr7 oil pressure relief valve fitted as well? does the zephyr motor have the oiling ports to the pistons as well?

diamondnik wrote:

What Injected did works for aftermarket radiators.  But I'm using factory and the port ID corresponds to oil line ID.  To change volume through the oil cooler would mean to change the entire system with something that has larger lines, and core piping.  Regarding oil flow, I'd like to remind that there is a diameter reducer - oil jet - at the base of the cylinder and also an oil jet between the top of the cylinder and head.  Both of those jets are much, much smaller and increase overall pressure in the head.

Understand completely, my concern would be the factory set up isn't intended to carry 100% of the oil "flow". Ultimately it's only my opinion and you need to decide what you are comfortable with 

Looking at the initial picture posted the cast hole restriction that separates the two cooler lines has been engineered to adequately feed the factory oil cooler. Kawasaki does not do anything haphazardly.

Just judging from that pic it looks to be about 1/4" diameter, just enough restriction to divert the flow without having to have a plug in there. Yes there is a bit of leakage between the circuits but that is just a engineering compromise.

In the past when I installed a oil cooler on a 650 engine I put fittings on the main oil plug under the points cover and one on the oil pan drain plug. Once I had a GPZ750 pan I liked the idea of having front mounting fittings. This makes for shorter line lengths and a cleaner installation.
 

I also used a zr-7 oil pan for my kz750e motor as it has the oil cooler ports, but no hole for the oil level sensor. (The E motors never had the oil sensor)
My oil cooler is always very hot during operation. 
I admit that I never noticed the bypass in the oil cooler ports as I never had another oil cooler pan to compare it too. 
I have to note that I am also using the high volume zr-7 pump and oil pressure release valve. The release valves between a kz and zr-7 have different pop pressures due to different oil pump pressures. 
I suspect, and as others have hinted at, the zr-7 oil pan has the bypass due to it having significantly more oil flow that the oil cooler cannot accommodate. So the oil flow is so great, that it will force the majority of oil up into the oil cooler and the excess oil bleeds off into the head along with the cooled oil coming from the cooler. 
So it is possible that kz oil pumps do not provide enough flow for the bypass design and that causes most of the oil to bleed straight up to the head rather than take the path of greater resistance into the oil cooler. Hence the oil cooler never really getting warm. 
 

Rangeroy, I'm using the ZR-7 oil pressure valve to complement the high volume oil pump.  Regarding the cases, Zephyr engine doesn't use piston cooling jets, only the ZR-7 cases do.  I'm using the ZR-7 cases because I wanted the benefit of improved piston cooling, otherwise I'd just use a GPZ engine.

Daftrusty, the Zephyr and ZR-7 use same oil coolers and oil pans but different oil pumps and pressure valves.  I presume the reason is because the ZR-7 engine cases use 4 piston cooling jets which require higher pressure.

Everyday a school day with these motors