Cool thread! Telescopic covers are one piece of equipment that I always build myself, the ones sold by suppliers are too shallow for my needs. I also make them a bit wider as well to accommodate tar paper or foam around the hives and still place them over.
For the tops, T & G "car-siding" (the mostly yellow pine used to enclose freight cars) purchased at any lumber yard is comparable to plywood in price without the potential worries over what's in the plywood, especially exterior grade or treated. Sorry...it is a personal concern but s/b considered.
I use 1 x 4 for the sides because they provide the deeper overhang necessary for my vent/feed boxes which are reversed depending on the season, square it, screw it, paint it and cover with any kind of metal. They last for years.