After hearing back from several people that the challenge is moving too quickly after your Sim starts earning more money I have decided to make the following change to the moving to a new apartment rule:
You must stay in every apartment long enough to pay the first week’s rent. You cannot simply move into one apartment and then quickly move into the next if you can afford it! This will prevent the challenge from moving too quickly.
I hope this helps everyone find the challenge more… challenging! Let me know how this change works 🙂