I want to thank everyone for their replies.

I've done a lot of thinking and a bit more riding since I first posted, and you have helped me realize that the bike really is not as much of a problem as my level of fitness (or lack thereof!). Every ride gets easier, and I think a switch to some narrower tires is going to fix me up just fine for the foreseeable future. If I continue to ride and improve my stamina and strength, I can upgrade to a better, faster bike. I now see that as being further in the future. I want to work on "earning" it.

FWIW, I think I figured out the problem with my knee "clicking". I did not have the problem until I raised my seat, but there is no question that my seat was too low. I think that since this "comfort" saddle is so wide, and my legs are so short, having the seat raised up makes it impossible for my legs to pump up and down in the correct vertical plane. The wide seat forces my knees outward. I am going to look at a narrower saddle, and I think this will solve my problem. Until then, I have lowered the saddle back down so I don't injure my knee and wind up completely sidelined.