It's my opinion that, before you try any other suggestions, you should focus on nailing your speed, and better use of trim, in that order.
My landings got so much better when I accepted nothing less than nailing my approach speed. Look in the POH yourself. It may give a speed range, probably 60-70 kts or so. Take the lower number (assuming calm wind), and absolutely nail that speed on final. Accept nothing less.
Make a smooth round out, hold it off as long as possible, and then see how you've done. There's a good possibility that speed control is nearly the entirety of your issue, and my hunch is based on your admission that you generally shoot for 60-70 knots. I did the same thing, and you know what? It caused sloppy flying. 60-70 meant sometimes I came in at 70ish. Maybe it was 72, but at least I was close, right? That's way too fast in these 172s. Caused me all kinds of trouble. The plane isn't ready to land, it floats, you're in the air longer which means more time to screw things up, you're landing flatter, you get antsy and want to set it down, you give up on the landing because it's taking too long, etc. etc.
I'd give it another go with the same instructor. Pull out the POH before hand. Take a look at the approach speeds. Tell him/her you'd like to try nailing 60 knots and see if your landings improve. He/she will likely not protest, because after all it's right there in the POH.
Nail your speed, get your trim in, see how you do, and let us know how it goes.