] Yes, it's ironic that it would have been the perfect time, for Claudius is not really seeking forgiveness, for he knows he doesn't deserve it, but Hamlet has no way of knowing this.

Yes, I should have made that clearer in my previous post--the great irony is that it is the perfect time to strike, if Hamlet had known Claudius' true state of mind--which, as you point out, he doesn't. It's a bit for us to appreciate as the audience; we're the ones going, "Oooooo, if only."

] "No reckoning made, but sent to my account
] With all my imperfections on my head:
] O, horrible! O, horrible! most horrible!"

] Hamlet wants Claudius to suffer the same horrible fate, and he believes he won't if he is killed while in prayer.

And yet another bit of gruesome irony: Claudius might actually have been better off--according to this--if Hamlet had killed him then. As things stand while Claudius is trying to pray, he has committed one murder (that we know of!). However, shortly after that, Claudius is laying plans to have Hamlet murdered when he sends Hamlet off to England. So, Claudius is seeking forgiveness--or at least, relief from the nagging of his conscience--over one murder, but planning another. Guilt follows guilt from there on, so that when Claudius finally does die, he has MANY more "imperfections" for which to account.

And then, bypassing this opportunity is part of Hamlet's tragedy as well. Hamlet murders Polonius, which leads to him being sent to England. On the way there, he arranges the deaths of Rosencrantz and Guildenstern for what he perceives as their betrayal of him (and to expand on the point you made, he specifies "not shriving time allowed" when they are put to death). Ophelia goes mad and dies; Gertrude dies drinking the poisoned cup meant for Hamlet; Claudius dies at Hamlet's hands; Hamlet and Laertes kill each other . . . death after death, all traceable to that scene in which Hamlet stays his hand with Claudius but then impulsively kills Polonius.