Here are a few photos, we have reconditioned quite alot P22's in the past. As I remember the construction was 1/2" and 3/8" marine ply. I think most of the panels may have been 3/8" but probably better to use 1/2" on it all.
Its easy to do, getting the old screws out of the sheets below the panels is the hardest job. They are brass and turn to cheese.
For the hardest ones we put a small hole saw over and cut the surrounding ply out . Sometimes we did this on lots of them.
Dont use cheaper WBP ply, only use marine ply. The WBP ply on the market these days will not last. I used it once and i regretted it shortly after.
Do prime all the panels on each side before screwing it down.
The smaller panels that go on to the deck beams should be fitted with a polysulphide sealant, this will always stay slightly tacky. This was mod standard.
The larger panels that go on top are fitted with foam tape so that they may be removed again. Around the outside few mm a small bead of sikaflex or other polyurethane mastic is applied.
The larger panels are fitted with countersunk screws in to half cup washers (this you will see on your boat at present) the panels below are fitted with countersunk screws in to the ply.
I enclose a few photos, sorry they are not that great but it should show you some of it.
We stopped doing P22's some time ago, but I am doing a P38 at present, ill try and get some photos up of that soon.