Just one more follow-up comment. I must be dense, since I couldn't seem to figure out what you meant in your comments, Rob, but I got it now, so thank you again for your help.

To summarize:
With Flex Projector, I can't import my image and see it while I fiddle with the projection parameters. I have to guesstimate the results based off the earth map that is already there. Then when I do the Project step, it lays that projection onto my base image and gives me the tif file. When I open that in Photoshop, I can see it with the projection applied.

It seems a hassle if you can't see it to make adjustments. I think I'll be sticking to G.Projector unless there are reasons to do otherwise.

So, are there?