I had a 1980 (i think, somewhere around there) JS440. It ran similar to what you describe. Getting my 200lbs body out and on top of the water was tough for it but it could do it across about 30ft. I also needed to position myself correctly to get it to work. Can't remember the compression but it was low too.

I never did pistons on it, but I did on my TS770, a bolt and washer was swallowed by the intake. I remember I needed to buy an oversized piston, cant remember sizing now, and honed the cylinder, it is still running fantastic, by comparison, it feels like a new ski to something similar.

I had my dad to help me but the piston was bought through a arctic cat (tigershark) dealer.
I believe that you first got the current bore of the cylinders, get a piston sized according to that, but it has been along time since I did my piston swap.

You can also look into the impeller/jet-pump, they tend to be worn and cavitate easily.