Thanks very much for all the replies. I had been trying to fold to all-ins with just TPTK or an overpair as a general rule, because so many people love to push all-in with two pair or whatever. But I have been gunshy.
No more!!
Last night I have a similar hand except with AA: jack it up and get 3 callers again. This time I'm 3rd to act on the flop and it's the 2nd guy who goes all-in on a 442 flop. I had a pretty big stack, as did the guy on the button. I tried to convince myself I was beat but I flat called. The button thought and thought and thought and called also. Turn bricks off, I push the rest in, the button calls that too, and I basically triple up against 99 and AK. Sweetness!
I credit my call on the flop to reading what you guys said here about reasons to call. Thanks again.