I have had *great* success in reducing color print contrast by "pre-flashing". By that, I mean replacing *some* of the light forming the image with neutral grey-card light: If the exposure for a print "analyzes out" to be 20 seconds, I will modify that to a "pre-flash" of 5 second of a grey-card image "balanced out" and 15 seconds of the original exposure - also balanced out.
This sounds a lot more confusing than it actually is in practice. The idea is that an overly contrasty image is both TOO white and TOO black ... so the grey image will LESSEN the "white" AND the "black".
This is one of those things that I thought about and reasoned out - it made perfect sense THEN - but I'm having trouble duplicating the thought process NOW. I know that it DOES WORK to lessen contrast - I haven't really needed to increase contrast with color film.