Flash,
While I understand you don't like juggling buckets, let me throw this out there for you to ponder.
Try and invision seeing a person under water in a pool. If that person has hair (LOL) it will usually float upward, and/or side to side as the person moves around. Their hair suspends and doesn't lay against other hairs.
If we apply this analogy in the same manner to fiber washing mitts, only on a much smaller scale, this suspension allows the fibers to have more space between other fibers. The dirt particles when agitated against a grit guard then tend to float free and away from the fibers.
Blasting with a hose, while it could work to remove some of the heavier particles of dirt, will not remove the lighter particles of dirt trapped in the fibers. The only way to free them would be to place the mitt under water, suspending the fibers, and at the least sloshing the mitt around if a grit guard isn't available. In fact, along with agitating against a grit guard or something similar, I would add that I think it's also important to slosh the mitt around after contacting the GG.
Call it over thinking things, but if you add dirt to a glass of water and then slosh the water around, some of the dirt particles will remain high in the water column until being allowed to settle, which will not happen in a short amount of time.
Depending on how particular you, or a customer would be, determines your approach. I prefer to err on the side of caution.