Time dilation is said to be already infinite at the event horizon, so how could it become stronger inside?

Yes but that's seen from the outside. When you fall in you don't exoerience local time dilation. Only global time dilation, between you and the positions in front and in the back of you. So you only see tidal force.

Time dilation is said to be already infinite at the event horizon, so how could it become stronger inside?

Yes but that's seen from the outside. When you fall in you don't experience local time dilation. Only global time dilation, between you and the positions in front and in the back of you. So you only see tidal force.

What takes millions of years on the outside takes little time on the inside. If you fall in you are radiated away by Hawking radiation fast. On the outside it takes millions of years, if not more.