The backing plate I have is not the 982D that was specified by Simplex, but a 982B. The only real difference I could see was no spot on the back to secure a bearing. I remedied that by machining the plate to accept a bearing adapter that I also machined. I used a light press fit and some sleeve retainer to lock it in.
Here is my method for installing the piston. I oil up the piston and rings, then tighten a band clamp just snug enough to completely compress the rings. I then lay the assembly upside down on the bench, as shown in the picture. I then give a swift tap on the end of the rod with my hand and push the piston right into the cylinder. As the Brits would say, “works a treat!”

If anyone has a sharp eye, you might notice I do not use a standard ball bearing in the rod. I use a needle bearing instead. The reason I do this is because the available bearings these days have either less balls, a plastic retaining ring, or both. I was introduced to this conversion by Bob Kerr, but his version used a different sized bearing and needed his custom rod. The late Ernie Bulter found this bearing, fits a stock rod, and just needs a custom washer to make it work. BTW, that is one of Wayne’s billet rods that I install a bronze bearing into the small end.