The ending makes no sense.
Why is the time-displaced Picard compelled to go back on the shuttle? The real Picard says "the cycle must stop" and shoots the other. What cycle? The real Picard didn't decide to leave the ship while Riker looked like the recording showed, so the cycle was broken. The time-displaced Picard tried to go instead, which would have been a "grandfather paradox." By trying to go, he broke the time loop himself.
And if it was this same Picard who went through the loop over and over, he would have aged into infinity if the loop continued.