I kind of agree. It would be interesting to get an explanation from the OP as to why he believes some of his pistons are "backwards".
Pistons need to be installed in the correct "direction". Ie, "this way towards front of engine". There is almost always a mark, notch, dot, arrow, etc that indicates "front of engine" as installed.
There are several reasons that there is a "correct" direction. Dome shapes that only fit into the chamber one way, valve pockets, connecting rod offset, and on flat-top or dished pistons, most importantly: The pin hole is NOT in the center of the piston. It is off-set to one side to promote rock-over at TDC with minimum wear, stress, and noise.
I do a lot of engines for inboard boats. Vintage twin-engine installations often use one "opposite rotation" engine to achieve counter-rotating propellers. It is achieved with a different camshaft driven by a two-gear drive, starter motor, and crankshaft oil seals. Not much else.
I once built a pair of 283's for a 1963 Chris-Craft. I instructed the machinist to hang one set of pistons "backwards" on the rods for use in the counter-rotating engine. He felt it wasn't necessary or "correct". Although I had never seen instructions to do this, I felt it made sense based on "what I know about this". I insisted, and he did it. When I tore down the original 1963 engines, sure enough, the counter-rotating one had the installation notches facing the REAR. I felt exonerated. Turns out my 'instinct' was correct.
What do you mean by "backwards"?
DaveP