Dirt and leaves might be too dirty for a rinseless, but I take from this post that bucket washing with a hose is not a preferred option for you. I use rinseless method a lot (GDWM) with a variety of rinseless products, and D114 is my current favorite. Its a great value if you are going to use a lot of it.
I would be very hesitant to use Costco towels on paint, even for rinseless but its just my preference, others have different opinions. The absolute best towels I have ever used for rinseless are the MM 800's but they would be cost prohibitive for a business. I also have a lot of 530's and 600's that I use as well. I prefer a dual plush towel since it gives you both plush sides to use, and IME the plush side works better for initial pass with rinseless. The dual plush 600's, which I believe the Chinchillas are, are available at MFT for a very reasonable price if you are buying in quantity. Also their 530's are excellent towels at an attractive price point, but they are not dual plush.
I have found that with a GDWM, where you pre-soak, then make a pass with a wet towel, and then go over it with a damp but wrung-out towel, the MM 800's are absolutely amazing for that second step, they take out almost all the water with one wipe of the damp towel, which saves time and effort to get 90% of the remaining water off. Again, cost is a factor, but the result of the second step are amazing. You would only need a couple of those, and use the towels of your choice for the initial wet wipe.