Often misplayed situation

Here's a situation I see a lot of beginners misplay. Let's derive it from this situation:

7-handed blinds: 100/200
BB: 2200
Hero: 1100
BT: 3000
CO: 2000
LP1: 3000
LP2: 1200
LP3: 1000

You are pushing any two here, obviously, even if the BB will call with the top 20% of hands.

Now, let's say your chipstack and the BB's are inversed.

7-handed blinds: 100/200
BB: 1100
Hero: 2200
BT: 3000
CO: 2000
LP1: 3000
LP2: 1200
LP3: 1000

With the same calling range for the BB, you also push any two. This may seem like a waste of a decent chipstack, but adding that 200-300 to your stack is important.

Now let's add about 1000 to both stacks, with the same calling range.

7-handed blinds: 100/200
BB: 1900
Hero: 3300
BT: 2000
CO: 1000
LP1: 3200
LP2: 1000
LP3: 1000

Here you are the bigstack and are in a great position. Pushing any two would be a very bad play, simply because of your chip stacks. If you push and lose, you are in a terrible position. If you push and win, you are in no better a position than you were before.

If you're trying to decide whether to push or not and don't have time to open SNGPT, just ask yourself - how much will winning these chips help me? Do I have a real shot at getting ITM if I don't win these chips, without catching aces or kings or some other good hand and doubling off of it?