Well, in theory, you are right. In fact, your imaginary ship doesn’t need to go 60 mph, it could go 1 mph, so long as it could keep up providing the thrust to maintain that speed against the pull of gravity. Unfortunately, we don’t know how to build a rocket that can do that. They would run out of fuel and be pulled back down.

Escape velocity isn’t how fast you need to go to escape gravity. It is how fast you need to go to escape gravity WITHOUT PROVIDING ANY MORE THRUST.

Escape velocity from Earth’s surface is 11.2 km/s. If you are already in low earth orbit, it’s a bit lower at about 11 km/s. If you’ve made it to geostationary orbit, it’s a lot lower – 4.78 km/s.