So, here's what I did to them:
I then sewed these strips onto the top raw edge of the shirt in 4 sections (1 across the top front, 1 across the top back, and 1 longer strip around the curve under each arm). After this I folded them over and sewed the loose side of the strips down to the seam allowance I just created forming channels. As you can see, I left openings at the top front and back points of the shirt (for a total of 4 openings). The back of the shirt looks exactly like the front, minus the Uncle Sam kitten.
I then cut strips to make ties with. I used 4 separate ties. Two ties were threaded through the channels that run under the arms, (1 under each arm) and 2 were threaded through the top front and top back of the shirt (1 in front, and 1 in back). Where the ties met at the openings, I tied them together, adjusting the length for a good fit. I then tied the remaining lengths of my ties together on my shoulders to form straps and trimmed the excess. I later went back and hand-sewed the channel openings closed around the ties and sewed the bows on the shoulders together so they wouldn't come undone.
For my daughters shirt, I started by cutting off the offending stained part of the t-shirt. Since her shirt fit just fine, I didn't have to do as much altering to it.
I cut out a long strip of a cute polka-dotted fabric (it was twice as long as the circumference of the bottom of the shirt), narrow-hemmed one side of it, gathered the other side of it and pinned it to the bottom of the shirt. I then sewed this piece to it. That was it!
And here are the finished t-shirts! Not exactly "matching" but pretty close. My daughter loves the ruffle on hers and my tank top fits a lot more comfortably than the little girl's t-shirt did!