I made a cooler set up for No Problem last June.
I used a Jabsco pump like yours and it would cavitate once the shirt was hooked up.
I used longer lines than I needed in case someone tried to get out of the car before disconnection, they wouldn't get hung up or damage anything. The longer lines many have increased the probability of cavitation.
I could suck on the return line or mess with the pump to get the thing to flow and it was okay. Unfortunately, it did not just work by simply turning on the switch.
I bought a small Rule pump like Cool Suit uses but have not tried it out.
Another consideration is the size of the cooler. My friend has the small round Cool Suit cooler in his Miata. It's only good for about a sprint race.
Block ice last longer than cubes. Floating blocks of ice are heavy and may destroy the pump.
I used a larger cooler to increase the life of our ice since we try to run 1 1/2+ hour stints.
In my case, 1 gallon antifreeze jugs fit nicely in the cooler I used. We could easily put 3 in the cooler. I stood them up inside and ran a string through the handles and tied them to the far side of the cooler from the pump.
Having blocks of ice in a container allows you to simply swap jugs without have to drain melted water to add more ice.
We did use some cubed ice with the jugs cause it I think we were low on frozen gallons.
Other than the pump cavitation, it worked well.
Troy
#35 LRE
1973 Datsun 240Z