> 3. However, from the past experience with physics, we know that mathematical infinities or singularities are often just an evidence of the theory breaking down. So perhaps it's the case here, and a more complete theory will allow to work around the infinity somehow.

Then it won't take infinite amount of energy, just (infinity minus one). Also, how do you stop? need another near-infinite energy?

But also also, due to time dilation and length contraction, wouldn't you end up in a 2d universe where time doesn't pass for you?