My situation was somewhat similar to yours. MDF drawers in a very fancy new bedroom set. I did not know this since my bride made the purchase without me.
The drawersw started to fall apart and I wanted to fix them properly. Using the Kreg jig I made drawer boxes first out of 11X6 white wood. Then I tried cedar (love that smell). Since this was my first project with jig I was apprehensive at best.
After finishing one dresser my wife opted for cedar all around. I have since used the jig on all sorts of tings, but the drawers?
save yourself some grief and use wood rather than composite. it will last longer, smell better and is easier to used.