Party "Hellkat" SnG analysis: Problem with split pots

[FoldALot.]

I'm trying to study some of the most common endgame problems in the new PartyPoker "Hellkat" SnG's.
These are time-based one-table tournaments that end after 15 (or 30) minutes, and payout is based on the final chip standings (payout is 50/30/20 as usual). So often you will have a final hand where the short stacks have to move in no matter what to have a shot at a top 3 finish.

Here's an example:

Blinds 150/300. Clock indicates that this will be the last hand.

UTG: 3800
Button: 5000
SB: 4200
BB: 7000

UTG moves all-in, of course the correct play.
The button is in an interesting spot here. If he decides to play then SB might fold for 3rd place and BB might fold for 2nd place, so he would end up playing for 1st or 4th. If he folds then he's very likely to finish 3rd. I will have a closer look at that, but here let's say he gets dealt 32o and folds.
SB realises that if he folds, BB will fold as well and he will end up 4th so he's forced to play his random hand.

Question: Which hands should BB be calling with?

If BB folds then he will finish 2nd unless there's a split pot between UTG and SB, then he will finish 1st.
Pokerstove says that in a showdown of two random hands there's a 4.06% chance of a tie. So if BB folds his equity is 0.9594*30+0.0406*50 = $30.81.

If he calls it gets complicated.
He will finish 1st if he wins the 3-way showndown or splits the pot with either one or both opponents.
He will finish 3rd if one of his opponents scoops the pot.
And he will finish 4th if his two opponents split the pot.

Now how can I solve this? I need to know how likely each outcome is for specific holdings of BB. I don't think Pokerstove is capable of that. Is there any other software available for this?

Thanks in advance and sorry for the long post.