I'm in for the night, and I don't know if the spaces are similar in the Model 3 as compared to the Model S, but I have coolers in both spaces. I will check tomorrow morning, and get the models for you to test out. As I recall, in the frunk, there is an Igloo brand marine cooler that fits nicely. It has the benefit of not having a drain plug, so I don't have to worry about leakage. I think that the model may be out of production, but I'll see in the morning. I've had that one for 10 or so years.
As for the rear, Coleman makes a low profile cooler that fits, and the top mat can rest in its normal position. It also has no drain. (I looked it up on the Coleman site, and I believe that it is a: Item# 3000000452, 24 Can Party Stacker.) I'll double check in the morning.
We don't use that back one very often, but the front one is good on trips. On one of our trips through the Great Smoky Mountains, we stopped at a pullover to make lunch. There were some folks on a rise behind the car at a picnic table. My wife made a sandwich for me, and, as I walked away with it, one of the ladies called out, "Hey, are you all frying bologna on your engine"? We laughed, and educated them.
If you don't hear from me in the morning, check in, I will mark this thread so that I get updates on it. By the way, ice holds admirably in the frunk ice chest, in spite of the heat.
Bob (in Louisiana)