Friday's hand revisited

I cant stop thinking about this hand... You are chip leader with 36 / 1800 left and have JJ in MP. You raise to 15k (2.5x) with 500k behind. The cutoff makes it 40k. With $300k, the cutoff has an above avg stack and is the second largest stack at the table.
OPTIONS:

1. Chip value (DV) is very high now. The avg stack at the final table should be about $500k, which you already have. There are plenty of shorter stacks at the table. You can fold here with little loss. But what does that say to yourself? To your opponent?

2. You can call, avoiding running JJ in QQ, KK, AA. But will have to play post-flop OOP. You could also check-fold the $40k and still be the chip leader.

3. You could raise to $120k, but this creates a pot odds issue. Unless he is on a re-steal, he calls here and now you are playing a $250k pot OOP. In the case he is on a re-steal, he may (probably) fold.

As I weighed my options, I did not give enough credit to #3. AFTER the bubble, especially "down the stretch" (as they say in horse racing) with 5 tables or lss remaining, players start using the re-steal more often. But I did not think of this for a couple of reasons:

A. I had not been re-raised like this yet at the table, nor had I observed any re-steals.

B. We did not have similar stack sizes. Its rare for the second largest stack to re-steal from the big stack.

As reported, I opted for Option 2. I wanted option 1, but did not want to be weak, be perceived as week, or fold a premium pair because I didn't have a pair. Not the best of thinking, but honest. But I picked #2 OVER #3 because I did not want to get re-re-re-raised all-in by AK and be forced to race.

The flop was, as reported, 443 (two toned).

Now, I have an over pair and the pot is $90k or so. Again, I have options:

1. I can bet out my overpair and expect hands like AK to shrivel up and fold.
2. I can check and wait for the aggressor in position to make his play.

I opted for #1. I feel this was the real, fatal mistake.

A. I bet $50k, and made the pot $140k. The pot is becoming epic. All I have is a pair that may or may not be bigger than my opponents hand.

B. I did not respect position enough in this hand. I really believed he had Ax and I was ahead. My hand read was good, but my luck was bad.

He moves all in now. Options:

A. I can fold and keep my chips, avoiding throwing valuable money away. I have lost $90k and still have $400k and be 2nd or 3rd in chips.

B. I can call because I beat so many hands here and I feel he is resigned to his fate.

Before the late stages of +EV. But LATE in the tournament, down the stretch, one must look for these potholes. The EPIC bloody hand that may be a turned set, or top-two played tricky, where players are trying to trap and extract max value.

I think I need to continue thinking about this...