Do you have to be stealthy about your grow?
if no, then what you could do is take out the closet door, by un screwing the hinges. Go to homedepot and buy a sheet of styrofoam and turn it into a door.
Buy velcro from a dollar store, and tape it along the wooden door frame and attach the styrofoam to the door frame with the velcro.
Cut holes in the styrofoam and pull air out of your closet and exhaust it out a window with a fan and some ducting. You can also bring fresh air from your room into the closet.
When you need to get access to your plants, you can pull your styrofoam door away from the door frame and work on your plants, when your done just attach the styrofoam door back on. Attach mylar to the inside of the styrofoam door to help reflect light.
Velcro is strong, so when you pull the styrofoam away from the door frame, dont use too much force, your styrofoam door will snap and break. Take a pen and run it along the edge of the door frame to seperate the velcro from one another and then gently remove the door.