How to mount a 2″ mast to the side of a utility pole

NRG greenboard is 98% air and therefore only 2% polystyrene

NOTHING can be mounted TO this. Your reel may be mounted THROUGH it to the studs behind.

From the Greenboard handbook:

17.1.5 Solid Blocking of Fitting and Accessories Consideration should be given to the installation of wall mounted accessories i.e. taps, electrical fittings, etc. It is important to allow for adequate backblocking for these items prior to the installation of the NRG Greenboard™.

Since this didn't happen, you have to add the blocking EXTERNALLY.

The typical 50' hose full of water is at least 15 pounds, the reel another 10 pounds and the pulling on the hose another 25 pounds or more, so you need a sturdy solution.

You would do well to distribute this across 2 studs, perhaps using 2 2x4 treated lumber. The screws would need to be long enough to go through the boards, outer covering (I hope the house isn't only covered in greenboard), the green board and at least 1" into the stud. Weather proof decking screws (ceramic coated for rust) would be a sturdy choice and come in 3", 3 1/2" and 4" lengths. All screw holes should be pilot drilled and filled with an exterior caulk or an exterior silicone.

Once the support boards are mounted to the studs, the reel can be attached to the boards with the original hardware.

Plywood is a lamination of several layers of wood set with the grain rotating with each layer. This actually helps resist warping, but does not eliminate it (as you can see). This happens because of some flexibility in the glue that allows a gradual creep.

The usual solution is as you suspect - laminate the plywood to something else. This could be a metal bar, either aluminum or steel. Perhaps the most effective would be angle stock (metal forming an "L" in cross section). A flat edge of the angle is screwed to the back. The perpendicular edge then acts as a brace.

If you do this, you need to first flatten the piece as much as possible. I would recommend placing it face down on a flat surface, possibly with a sheet below it to protect the art surface. Then weigh down the corners with very heavy weights, such as full paint cans or barbell discs. Lay an angled bar across the full width near the top and another across the bottom. Place screws every 6 inches. The screw length should be long enough to go through the angle stock and 3/4 of the way through the plywood.

You can then rehang the piece using a wire threaded through holes at the ends of the angle stock. If you really need to use velcro, you could attach wooden filler strips to the upright edge of the angle stock, and attach the velcro to the back of these strips.

An alternative bracing can .be done with strips of plywood, al teast 3 inches wide and 3/4 inches thick. These can be glued and screwed to the flattened panel instead of the angle stock. If you use a strong wood glue, such as Titebond Ultimate, this will help prevent creep, as will the screws.

The advantage the angle stock method is that it is reversible (no glue).