Im not sure if this is known but, if you keep behemoth on the front side then after you kill him, go to the heartless symbol, it should despawn him fast enough for you to be able to open the menu. Could this be viable?

Runners have figured out a way to heal without the menu. Sure, you're down a mega elixir for final battles but it doesn't change too much and opening the menu would be slower. However, if you feel that you need the extra mega elixir for World of Chaos, then sure, opening the menu to use a cottage is completely acceptable. Just know that it is slower by a few seconds.

I just know that on ps3 they used to use the menu

That's not entirely true manny.

The blue menu is actually faster because it allows us to skip grabbing an extra elixir and we don't have to worry about menuing it in at some point. Plus we already have a second cottage from the blue trinity in Hollow Bastion.

The reason we don't open the menu in the PS4 version is that it's basically "frame perfect". What you actually got by opening the menu there was essentially a frame perfect pause in order to open it. This happens because PS4 speeds up the loads so much that it's very difficult to get the pause consistently as the game loads straight into the final rest fights. The position of where you kill the Behemoth doesn't affect it in any way as it all loads the same, it's just sped up a lot.

quite frankly we don't even need the elixir in the green room anyways, most people seem to skip it from what I've seen.

Eh, I might be wrong but I still don't think it matters which strat you choose there.