The obvious way to get around that is to hover above the ground so you don't leave footprints and to not hunt when it's windy, avoiding the problem entirely. It's quite possible that he didn't have a solution worked out for avoiding being exposed by airborne dust.
I'm not saying he has no solution. You are suggesting he has the ability to get around a hazard that is inherent to his nature. That's like suggesting that someone who regularly goes swimming has a way around drowning just because they go underwater. Yes, it's possible that a swimmer has scuba gear and could go underwater without worrying about drowning (in the short term, anyway). But it's much more likely that they just hold their breath.Other can also Hollows also kick around dust, when moving or while fighting.
Again, banking on him not having a solution to a common environmental hazard is a rather suspect decision.
Actually, yes it does. If he's invisible, we can't see him either way. If we kick up enough dust to blind everyone's view of the area, than he's blind as well.Also, even if it did work, kick up enough dust and Shiroksaki is blinded as well and limited by how far he can see. Which doesn't help.
But... But... PapaYou've gotta be kidding me, where gonna go see Ichigo's dad? Even if Isshin is gaining back his spiritual power, I'm pretty sure he doesn't know how to use it in a situation like this, and Tatsuki's soul is being messed up by hollow stuff, something Urahara can deal with. Isshin is a choice that is highly likely to fail compared to Urahara or Ryūken even if we do end up owing a favor or getting killed.
We are once again taking the cautious route even though that almost always ends up making things worse.
EDIT: Made it more constructive