Just for the sake of conversation, shouldn't the pick up screen stop any debris that could be in the cooler from entering into the oiling system from the oil pan?

Absolutely not.

It'll keep something large enough to have it's own part number out of the pump but the smaller stuff will go right through. The only reason I was considering reusing my coolers is that I cut my oil filters apart after I removed the motors and they were clean.

Teague cooler is the same way as you can tear it down and rebuild. As others have said, regarding a cooler that cannot be disassembled the money saved isn't worth the chance that murphy is going to make you pay in the thousands.....

I have a friend that reused his cooler after trashing a crank with no problems, but he had oil filters before and after the cooler.

Not saying it is the right thing to do.

Ok, let me tell you about MrCool. I ordered two coolers from him to be shipped overnight and was going to use paypal. For whatever reason Paypal wouldn't let me pay him using instant transfer from my bank acct and I didn't want to use a credit card. So MrCool, or Russ who owns MrCool, sends my coolers to me overnight without payment. Told me just put a check in the mail. How can you beat that kind of service? Thanks to the guys who recommended him.

That's Russ! I believe he did a special Saturday drop ship for me. Class act all the way.
And great prices.

Glad he took care of you, have bought Afew coolers from him and all have worked flawlessly. Good luck on getting the boat back in the water!