Even worse: the way to maximize how long you have before you hit the singularity, you should do nothing. Firing your rocket in any direction gets you to the singularity in an even smaller amount of proper time: the singularity isn’t in front of you in space — it’s ahead of you in time.
Keep in mind that all of this is for the Schwarzchild metric, which is a nice solution to Einstein’s equations in the sense that you can derive it on a blackboard. It can’t describe what we think of as a real black hole for plenty of reasons, including the major one that a Schwartzchild black hole has existed forever and therefore could not have formed in a supernova. You need a different solution for a black hole that has only existed for a finite time.
You only get one microsecond as you cover over half a light minute? Huh.
Don't we know about a bunch of black holes best measured in AU? Won't you have a good chunk of time inside those? Does time dilation work severely against you?