1st: Yah, I'd go with glue too if I couldn't access the backside where the screws exit. If I could access the back, I'd put a small piece of hardwood there as a backer and change to a SS wood screw.
2nd: Sometimes drawers have a mind of their own. I installed latches. They can be found in or near the baby section of most general stores. They are used to keep toddlers from getting into things. Installed, they allow the drawer to open maybe 1", you push down on the latch and it opens the rest of the way. I used one for the bedroom drawer that wants to bounce open all the time every trip getting in the way of the retracted BR slide. *CRUNCH* when extending. Hate that.