Seeking super hard ice
Soft ice would be "pellet" or "nugget" ice.
The "softness" of the ice is in the way the ice is made-it's kind of chewable and breaks apart easily.
You've probably had it and didn't realize it. You can't really buy it, it's made by a pellet or nugget ice machine, a place like Sonic would have it.
“Névé's dense cubes melt more slowly than traditional ice cubes and come in a variety of shapes: perfect cubes, tall cylinders and golf-ball-size spheres. There are even specially designed square cubes that won't crack or explode when worked vigorously in a cocktail shaker, ensuring the purest martini possible.”
Not entirely sure they still stock it, but Bar Keeper in Silverlake was carrying a specialty line of ice for cocktails. Different shapes, purified water, frozen "hard." Might be worth ringing them up to see if they still have it:
3910 W. Sunset Blvd., Silver Lake, CA 90029
3910 W Sunset Blvd, Los Angeles, CA