I wanted to mention one thing. The oil cooler looks very much like a heat exchanger from a boiler.
I have an old Worcester Bosch combi boiler that kept on turning on and off due to a temperature sensor giving a high value. The boiler was written off by a Bosch engineer due to the list of parts that he would replace (I had to fix it else we would have to get a long flue due to new regs - lots of money).
I'd had the heat exchanger replaced a few years back and after some research the temp sensor read high because the energy from the gas was not being transferred to the water quick enough and thus the temp at the exchanger rose above a threshold.....bare with me here!
So, I took the old exchanger and pumped Fernox DS3 acid solution through it. Fernox has an indicator in it that goes green if there is sufficient Ca Carbonate deposits to react with. I carried on flushing until the colour didn't change, bolted it back on and hey presto it stopped cutting out.
My point here is that an acid flush on the heat exchanger could remove any deposits preventing heat exchange. Fernox is nice as you know when you can stop but vinegar would do - just wait for any bubbles to stop or leave it overnight. A solvent could be used on the oil side (white spirit or cellulose thinners).
Add to it that if coolant and / or distilled water has been used any limescale deposits would be low to zero. I can't really see that replacing the heat exchanger is warranted - a clean would do + o ring replacement. Just my two pence worth and I wont be offended if I'm flamed!
Oil cooler
Boiler heat exchanger, it does have an inlet and outlet on the other side
If you do replace it I'd actually pay to have the old one picked up so I could take a look as I've only seen pics (I'm not after one for myself!).
Charlie