That's what I meant by 'Oblique seems to twist the image instead of merely stretching it'. The first Offset slider slants the image to the left or right while the second one slants it up and down. I need the selected images to firmly retain their shape while stretching only the bottom. I just need to extend the bottom, not twist anything.
ETA: I think I may have found a workaround, though, but if anyone can think of an easier way for me to accomplish this in the future, I'd be grateful.
For anyone interested in my workaround, I cut the white images, opened a new file, turned to full opacity, added a new layer, pasted white images, rectangle-selected the bottoms and stretched them that way. I then used magic wand to reselect the two images and pasted them onto the blue UV map. Seems to have worked like I wanted it to.