First of all, there is no singularity. That is a mathematical object not a physical object. It represents where our math fails. Also you don't even have a complete picture because there are in fact multiple mathematical singularities inside a spinning black hole and it is far more complex than you are probably aware of. You have a novice interpretation of it.

Secondly, for you time is not slowed from your perspective. You pass towards the center of the black hole and reach it at a normal rate.

You would definitely die before the black hole does.

Spinning black holes (which they all are)... https://youtu.be/kIbP2Sg8y18

https://youtu.be/-q7EvLhOK08