I'm the opposite of your experience.
Stiffer flex irons for me is always more consistent but lack of the regular distance, usually about one club short but more pronounced in the long irons 2-3-4, may lose up to 1 12/ club length. I could control the ball flight way better with the stiffer flex, disbursement pattern is much tighter.
We've heard golfers losing trajectory height when swing speed is lower, I have no issue hitting the proper trajectory ( and I'm not scooping it neither, never did ), my first instructor told me I had the "snap" through the golf ball.......
I have horrible time using a softer flex ( that's prior to injury and before I passed 60 ), inconsistent and big banana curve ( either way you flip the banana ). But right now I like the light weight steel shafts in irons either stiff or regular flex, a sign of losing strength not able to handle the heavier weight, sadly. I'm not able to go back to the gym for weight training, yet. Not even doing push up at home because of the injury. I could swing a golf club, just not like it used to be.
Right now, it depends on how I feel that week to determine favoring which set of clubs. I have a pretty accurate forecast of the changing weather from my injury, soreness and sting always foretell the low pressure. Talk about that, I might let some of the older clubs go. Not quite sure yet.
As for your experience of the mixed set of rental clubs, I hope it's of no charge to you. I would not pay for a set of rental golf clubs if the whole bag is a mixed flex. I had seem a mix bag of all woods in stiff flex and all irons in regular flex and that's acceptable if I were informed before I pay for it.