I swapped out my first tube yesterday and had everything installed in less than 10 minutes! I was a little bit shocked because I was prepared to struggle through it for at least half an hour. Checked the tire today and it still seems okay - I'll see how these tubes perform. I haven't tried Mr. Tuffy liners yet and I hear they are tricky to put on.

As for finding the puncture while riding, I was able to pump some air and feel for where the hissing was occurring. Fortunately I could find it and patched it up to enjoy another 10 miles before heading home. Thanks for the tire suggestions, everyone!