I booted back over to Windows and revisited the toolset I had downloaded. It is RMXTools:
I made a copy of the current data.img which was 8G and ran the tool on it. This time I was a little more attentive to all the steps. ;)
I ran a check first. I was getting something about needing to fix a journal so I clicked the button that said it fixed things and sure enough it said it fixed the journal. I tried the resize again pusing it up around 32G (the slider control without and edit box to allow you to change the value by hand is kind of weird, especially since it does not try to adjust to what I think of as common sizes, but okay). It cranked on that a while.
When it finished, I ran another check and it said it was okay. I moved my primary data.img to a subfolder and moved the new big one in its place. I booted over to Remix. My heart sank when it stopped at "checking data partition" (or something like that) but it continued after a few seconds (takes 4 times as long; DUH! :) ).
In the Remix environment, all the icons were in the right places (added some, removed some, moved them around) on the desktop and task bar. Opera (my current browser of choice; I can't convince Chrome to behave enough like a desktop to suit me) came right up and had my recent tabs and logged me in for email. X-plore shows me I have over 28G free.
So unless something is wrong that takes me a bit to discover, it looks like a pretty painless path to more space.