UPDATE: I coughed up the money and installed a Mishimoto oil cooler.
I just ran an event at Autobahn, but unfortunately, it didn't go so well. After a couple laps in the warm-up session, 3rd gear broke. All of the other gears seem fine, but with very little warning, I converted my 6-speed MT82 into a 5-speed MT82. I still ran a few laps each day because I need the points for the regional championship, but I had to be in 4th and 5th gear the whole time.
Since I was already handicapped from the broken transmission, I didn't feel like pushing the car and breaking other things too. I just ran a few "participation laps". Given that limitation, I'm ambivalent about the oil cooler's performance. The oil temperature stabilized at ~260 degF, and I was really hoping for more than a 20-30 degF drop over the Boss 302 cooler. I'm pretty sure that if I pushed the car harder on a hotter day, I would have easily raised the oil temperature by 10+ degF. I'll probably contact Mishimoto and see what their expectations are for this application.
Once the oil temperature was stabilized, there was still some oil pressure loss under braking, but it wasn't that concerning. The lowest it got was 51 psi, and that should be sufficient for the engine (in small doses).
Here is a graph of my fastest lap (in which the engine would be working hardest). Speed is in black, oil pressure is in red, oil temperature is in pink, and longitudinal acceleration is in blue:
I'll be limping the car through the final event of the year, and hopefully I get a new transmission for the spring. It's possible that I have the oil pressure under now, but I won't know for sure until I can push the car as hard again.
You probably broke the plastic piece on the shift stop. If you stick with the MT82 do the bronze pads and the solid stop and you wont have anymore problems out of it.
Adding multiple quarts of extra oil to the sump is questionable (My opinion). The easiest Band-Aid is an Accusump. I have used several and they work to keep steady oil pressure. Pre-start engine lubrication is a great added bonus.
Boss 302 Radiator is a joke - The only advantage is pre-oil heating for street cars on first start up in cooler weather. My opinion also.
A properly ducted oil cooler and slow opening remote mounted thermostat located away from exhaust heat is your best solution to controlling oil temps and street driving.
Please - Don't mount the oil cooler so it is on top of the radiator unless your radiator is massive - separate ducted cold air source is optimal so maximum radiator air exposure is possible.
Properly duct the radiator for best results. The stock configuration is not efficient
Fee advise is worth what you pay for it.
I will disagree on the accusump, These motors do not need them. I agree with Terry that the coyote has no issues at all with oil starvation. I have not seen or heard of one single oiling issue with the exception of the oil pump gears coming apart.