sleep paleo sounds like something you should be embracing. It isn't high in fat, its low in rubbish carbs.
The problem with your argument though is your use if good fats. I'm presuming you are meaning mono and poly? And therefore bad fat is saturated?
Except it isn't. That was a mistake made years ago by a man called cancel Keyes.
There have been a lot of studies since that say there is no link to heart disease from saturated fat.
Anyway, to get back to your question about high fat.
In order to be a fat burning machine, instead of a carb burning machine, you need to be in ketosis. If you eat medium or high carbs, you won't be. If you eat high protein, you won't be (see previous post).
Paleo is still a carb burning machine.
Your body prefers to burn alcohol first, carbs second and fat last.
Your body has about x amount of calories stored, when these are burnt, you need to refuel. Your body is not efficient at burning the fat stored in it. The analogy that helps you realise this, is thinking of a petrol tanker that has run out of fuel. It has plenty of fuel on board, but it can't access it.
Whereas someone fat adapted as access to y amount of calories (your fat stores) which literally lasts hours and hours longer.
There are roughly exact amounts in some literature but I've forgotten the numbers. I think its something like 2,000 cals from carbs and 20,000 cals for atore d fat. But I could be miles off.
This is the reason I don't want to do paleo even though I like it, I won't be in ketosis.
If you want to know how it works YouTube is a good resource and easier than reading pretty heavy science at times.
Look for
Gary taubes
Jeff volek& Stephen phinney (might be under the heading "the art and science of low carb performance)
The food revolution (the diet doctor)