I did this with my first grow and it turned out great. It will be tight if you wanna get 3 plants in there. 2 will fit comfortably with no problems. I have a door on my closet as well and it was alright. BTW, my closet is 2 1/2 feet wide and 4ft deep so I had to reach in to work my grow haha you will be able to work easier since they will be right there.

To solve your slat dilemma, just pick up a small roll of panda film and tape/tack it on the inside of the closet (black side facing the room and white side facing into the closet to reflect light. It will turn out good buddy, just make sure you get yourself some neem oil and a hot shot pest control strip to prevent any mite problems from arising. Watch the temps if you plan on using a HPS setup. Cool tube will help alot!

You will be just fine with 2 plant easy, 3 is a squeeze... But then again I let them flower longer