Asa, your post prompted a few more thoughts. I have used FastStone from time to time; generally the feature I use it for is its ability to correct timestamps. If I have taken a bunch of photos on my point-and-shoot whilst on holiday but forgot to set the right timezone (or even when there's daylight savings), FastStone can fix that easily. Only program I've found thus far that enables me to do that.
Regarding lossless JPG tools, the other program I use is JPEG Lossless Rotator (freeware). Very handy for correcting the rotation if your phone or camera doesn't automatically do it (or gets confused), as well as fixing any incorrect rotation flags (some phones set a rotation flag rather than storing the image the right way "up"; not all programs read these flags - especially when you upload to a website - so rotating the actual image is very useful in these circumstances).
