Slide-out tray fence with only a drill
Some table leg brackets and screws should be all you need, besides the rails which makes no difference in this concept.
Using table leg brackets will allow you to fasten and sandwich the pieces of wood material nicely with minimal unintentional industrial look. :P
4 Table leg brackets per drawer

Place one bracket on top of each corner of the plywood and screw to the plywood.

Next add the fencing around the sides and fasten with screws.

I was going to suggest other methods, like creating a table temp drill press in a table saw style and also using L-brackets but the more I thought of it, the more I realized this may simply be the easiest and best looking results. If you have any other concrens please feel free to ask. Cheers.