What distance are we talking about? If you're just off the green and trying to carry it 15-20 feet, landing just a few feet in front of the hole, it's going to be very difficult to get check that way. A big percentage of spin comes from club head speed at impact (assuming good contact), and you're just not going to get a low or mid height pitch or chip to check instantly carrying it 15 feet.
I also mostly use my 60˚ around the green (though 54˚ sometimes too), but I prefer smooth easy pitches that roll out more than 2-3 feet. I'm generally aiming for what you're complaining about, with roll out of 1-3 yards depending. When I really need super short check with a short shot I just try to hit it higher. You know the ball forward, more vertical shaft lean, use the bounce drill. The other feel that helps me is incorporating the "butterfly" sand shot style grip, with left hand a bit stronger and right hand a bit weaker. Also, to get it really high without going full flop, I'll sometimes put the ball well forward, set up with the face open, then hit it super wristy like some types of sand shots.
The other benefit of this is if you can hit it extra high you can swing harder, so you still land short but with more backspin, and I find this more consistent than a full flop shot, though still a bit risky from super tight lies.