When I do compression tests I find the reading keeps climbing the more I let it crank, up to say about 1 or 2 dozen cranks. But I see instructions say to let it crank only 4 or 5 times.

I always thought you should let it crank until the psi reading stops rising, but is that wrong? Should I just let it crank over a limited number of times?

Something is.wrong

Ive used many gauges, none took more than six pulses to .

I usually count 10 times. I put the gauge in a position where I can see it between the dash and the hood and watch it go up. 10 cranks and it usually is done. Good compression on a stock A series A15 is around 140-160psi. If all cylinders are with-in 10psi then your good. Others may have something different. That's just what I have found.

Could be worn bore/rings or ring lands. As the engine turns over more oil is thrown around and tends to seal the cylinder better.
Squirt a teaspoon full of oil in the bore and spin the engine up for 5 seconds without the plugs in it. Then recheck the compression. If it pumps up quickly you may have an engine problem.