You will never be able to get players to roleplay by force.
You can't just say "okay, and now for the next five minutes you all roleplay with each other." It doesn't work, you're asking for smalltalk between imaginary people that's the height of banality.
If you allow characters to develop actual goals, philosophies, and interparty conflicts players will automatically start roleplaying with each other. If you want players to roleplay with each other, you have to become skilled at engendering such goals, philosophies, and conflicts.
It has nothing to do with "downtime", enforced or no.