Maybe try a great white drying towel from Adams, and don't rub it on the car? Just lay it on, smooth it out, then pick it up and go onto the next spot.
I used to own a body shop, and on really soft, or brand new clear, the only way I ever found I could wash something without leaving lines in the clear was like this:
-lot of soap; I like Adams car shampoo or maybe duragloss 905
-rinse the car
-if you take take the nozzle off the garden hose and let it run on the car, the water will make sort of a funnel shape as it hits the car and runs off. Use the wash mitt in that funnel of moving water. You have to use a lot of soap and move the hose simultaneously with your wash mitt.
-My theory is that the layer of moving water floats the debris off the car as opposed to trying to encapsulate the debris in soap and then remove it with the rinse step. I'm not sure if that's true or not, but that's what I think.
Doing that, and then laying the microfiber drying towel flat, smoothing it out, and picking it up (no rubbing with the microfiber to dry) that's the only way I've ever been able to wash one and have it come out nearly unblemished.
It's especially obvious the damage you are doing when you wash if the clear is brand new. I'd recommend that everyone go buy a harbor freight spray gun, a pint of clear and hardener, and a hood from the junkyard. Put down two coats of clear, get it out in the sun, and wash it with whatever method you are using. The brand new clear is flawless from a micromar standpoint, and it's really easy to see what your wash technique is doing - good or bad.
To the OP:
Even if you have hard water at home, I would probably do it there with your garden hose. I like Adam's car shampoo, it's pretty cheap ($10 a bottle or so) and if it dries on the car it's not a big deal, it still rinses very well.
The rock chips should be filled, but don't sweat making it rust by washing it a few times.
2008 G8 GT - Grey / Black - stock on E85 & tune - 12.9 @ 106
2002 Trans-Am - Navy Blue Metallic / Black - M6 - Heads, Cam, N20 - 11.23 @ 127 - 525 RWHP
1991 Corvette - Black / Black - M6 - 383 - 11.37 @ 122 NA - No nitrous times - 415 RWHP NA - 550 RWHP N20
1989 Mustang LX - Gun Metal Grey / Black - M6 - Heads, cam, some other stuff - 12.57 @ 109