Interesting that you brought this up, because it's been on my mind for ages. Space wise, the forward section of Y both on the 3 class 777 and on the 380 is ideally suited to installing such a cabin.
But the real question is, like some other have posted - what kind of PE? I think the way it is currently offered in the market, it is a waste of money. 2x times the price of Y, with about 6-8 inches of extra legroom. Whenever I'm in Y on EK I have an exit row seat, so the added value of such a product is zilch.
A PE product needs to offer space - why pay 2x for better food, when the rest of the frills (check in, lounge etc) can be obtained with status anyway? So, I'd be willing to pay a premium for enough pitch that my seat goes lie flat, even if it is a bit narrow and at an incline, because that's much better than being stuck vertical for 10 hours.
Do that, and upgrade the J product to proper flat beds with direct aisle access and privacy. PE needs to have much more added comfort than a few inches of pitch - leg rests that go up, enough incline that one can rest properly, etc.
Conclusion - if they go down the way of a few extra inches of pitch - it should be part of the Y cabin, Blues can pay $100 per sector or whatever, elites get it free. Make it something significantly different from Y (but perhaps risk losing leisure J pax who downgrade to PE) and at least I'll pay a premium in line with the extra space I'm getting - by charging double you should be able to give me ~60 in of pitch, meaning lie flat seats.