In my opinion it would be a bit difficult without the right tools hence the awkward angles you would be working at . Because when putting the wood IN , you want it to be as solid and in place as possible therefore making it alittle hard to come loose.
Really any type of wood .. MDF or regular Plywood would do the job . As for the glue , IMO if you are possibly going to be taking these pieces of wood out in the future I would use like a window caulk with some screws to keep the wood nice and secure .. Then when the day comes to take the added wood out , all you do is take out the screws and give the wood alil yanking lol .