Here, the inspectors like to see a 4/10 hp pump dumping into a 4" line.
3" could maybe work, but a 2" is going to have issues. Once you go from pumped to gravity, things start to slow down.
Is there a way to intercept a larger line outside the foundation? Normnally you would find a 4" at some point. Or at least bring the pumped 2" to that 4" line.