From the description of the task, I'd say you need 3 sheets of 3/4 ply, 4 2x2s, 1 2x6 and a big box of drywall screws.
Make a square frame from the 2x6 that just fits into the hole. Cut 2 sections (lengthwise) from one of the sheets of ply that are the same width as the frame. Center the frame on one long edge of a full sheet. Measure from the edge of the frame where it meets the edge of the sheet to the nearest corner on the other long edge. Cut your narrow sections to this length. Cut your 2x2s to this length also.
Stand your frame on edge with a little bit (maybe about half) hanging out past the edge of the sheet. Mark the corners that are still on the sheet. Lay a 2x2 on the sheet from each of these marks to the nearest corner on the long edge. Clamp them in place. Flip the sheet over. Pick up the frame we left in place & set it aside. Screw the 2x2s securely to the sheet. Repeat this for the other sheet. (Don't repeat the part where we forgot to move the frame out of the way...)
Now the tricky part...
Screw the frame in place on both sheets where it was sitting to mark the corners. Stand the assembly up so the frame is on the ground. Lay those sections we cut earlier in on the 2x2s. Apply lots of screws.
Use some of the leftover ply & 2x2 bits to brace the structure. (maybe stiffen the bottom outer corners...)
Yup...works for me...
(Sorry for the rather pedantic description, I've been arguing with computers all day...)