I've tried a bunch of different ONR applicators over the years, including sponges, mitts and MF towels. I finally settled on the Meguiar's MF mitt. They're made of a fiber that grabs dirt, bur releases it easily. I have grit guards in my rinseless bucket, but don't rub the mitt on the guard. I make a pass with either side of the mitt, then just a vigorous shake in the bucket is enough to release the dirt and provide a clean mitt for my next pass.
I do use the Eagle Edgeless towels in my process, however. After completing a panel or two with the wash mitt, I wipe it down with the MF just to spread out the remaining solution and give it an "insurance" wipe in case I missed a spot. I'll use the same MF for the entire car, wringing it out as necessary, then following with either a drying towel or a spray of whatever drying aid I might be using.
During the nastiest times of winter, I may use two mitts, one strictly for the lower half of the car. My DD is black and after refining my technique over the years, I have no hesitation doing rinseless for the majority of my wash jobs. I use a pump-up sprayer with the same solution I'm using to wash and do a pre-soak whenever the car's salt-sprayed or just dirtier than usual.