Acoustical treatment is tricky stuff. It takes mass to stop sound and absorption that is designed to absorb whatever frequencies you need to tame. Your cardboard box might be doing well to block and absorb high frequencies but maybe you're still having some mid and lower frequencies get through (hence, the boxy sound). Also, you're right about the open front being a potential problem.
I suggest you measure your room response at the mic position and then speak with someone who knows a lot about treatment.
I'm using Real Traps mounted on mic stands placed around my room (thus, no damage to my walls, plus I can move them to where they're needed). I place quilts on mic stands behind the singer to help reduce sound entering the front of the mic.
Putting a throw rug under the singer might help. Be thinking about reflection points - you can do a lot just by placing a few panels in strategic spots. But, again, talk with someone knowledgeable about acoustic treatment and/or post in the "Studio construction & acoustics" thread.