It doesn't act at weird and once again. Most of the crew weren't paying attention. Mac certainly wasn't and was back to his own isolated and lonely self, until the dogs were attacked.That doesn't explain why the Thing is drawing attention to itself by acting weird.
Still early enough when they heard the wheezing.No, the dogs only start barking once the Thing starts weezing heavily, clearly exposing itself as not a dog. When Clark brings it into the kennel and the Thing calmly lays down in the middle (very suspiciously) the dogs are fine and none the wiser.
At this point you're just overthinking it and not what the script writers had in mind. There's only so much you can do. Especially with the technology and effects at hand in the early 80s. You can whine about it however you want, but I really don't care, so take it or leave it.If it's strong enough to dig that far under the ice in that short amount of time, why even hide at all? It could've just killed everyone through brute force alone. Or why not detach a small part of itself to hide in the ice, or any of the other numerous ways it could've done anything based on how it operates as an organism. It could've clipped its toenail and than have the toenail hide itself in Kurt Russel's beard till he rotated back to civilization