That's only if my feeble understanding of sbe and priority are correct.
Unfortunately, your understanding is not correct. Limbo's answer was the correct one.
The reason your understanding is not correct is because a player receives priority after spells and abilities are played and after spells or abilities resolve. So, each time you play a spell or ability, you regain priority in order to keep playing spells or abilities or you can choose to pass priority to the other player (CR 409.1i). That means, after you play a spell or ability and would get priority, the game will check for state-based effects. So, in this situation, you play the ability of the Triskelion once and it becomes a 3/3 with 2 damage on it (SBEs are checked, but do nothing). Then you play the ability of the Triskelion again and it becomes a 2/2 with 2 damage on it (SBEs are checked, and this time the Triskelion goes to the graveyard). You never get the opportunity to play the ability a third time.
So you don't simply gain priority and then play as many spells as you want and then pass priority, you actually are regaining priority after each time you play a spell or ability and have the option to either play more spells and abilities or pass priority. The game checks for SBEs every time you play a spell or ability.