Timing of playing Psyche!

Minion A enters combat with minion B via Bum's Rush.

Round ends and minion A's metuselah replaces Bum's Rush.

Can Psyche! be played after replacing Bum's Rush (regardless it if was in hand before replacement) or window gone since action has implicitly ended by Bum's Rush replacement?

Psyche!
[cel] Press.
[CEL] Only usable at the end of a round when both combatants are still ready and combat is about to end. After this round, begin another combat with the opposing minion.

Bum's Rush
Do not replace until after this action.
Enter combat with a ready minion controlled by another Methuselah. The acting minion gets an optional maneuver during this combat.

Here is the breakdown:

1) End of round phase. This is the time to play Psyche.
2) Round/combat ends. From that point, no more combat cards can be played.
3) End of action phase. This is the time to play e.g. Freak Drive.
4) The action ends. From that point, no more action modifiers / reactions can be played.
5) Replace Bum's Rush.

As you can see, the Bum's Rush replacement happens way too late to play Psyche.