You might try wrapping your cooler with a blanket or thick towel. My mash tun is a 48 qt igloo marine cooler. After the first couple of batches, I found that the lid wouldn't close as tightly and I could literally feel hot air escaping in a couple of spots. I started wrapping it with towels or...
What a coincidence. I'm in Denver for work and was about to post the same question when I came across your post. I'm interested in sours lately and getting ready to try my hand at brewing one so it looks like Crooked Stave will be a must visit for me.
I use a 1 gallon nylon paint strainer weighted down with glass marbles for dry hopping. I usually boil them both to sanitize.
Like the others have said, I wouldn't worry too much about contamination. Just open the bucket and drop it in.