DONE.
Updated both units to 3.01 using an external USB drive. The one I used was 64gb but I created a 29gb FAT32 partition on it "just in case" the updater was strict about using a 32gb or smaller drive.
it takes A WHILE to complete. But it's easy, prep the USB drive, turn off the TZT3, plug in the USB (into the white cable from the back of the TZT3) and power it up. Now... WAIT. It'll take a while and show a lot of things. But eventually you'll be presented with dialog box telling you to remove the USB memory (odd wording, but the point is clear). BUT you're not done yet. When it restarts it'll take several more minutes to finish it up.
As a side note, DO NOT randomly update any Maretron DSM410 displays you might have. I had some that were a pretty old version and attempting to load the latest one failed, and may have locked at least one of them. Though this is not a Furuno issue at all, just a warning to be careful about doing many updates at one time.
Where it IS a possible issue is knowing whether or not the latest release (of any device firmware) is suitable for loading onto whatever you've got in the field. My TZT3 were running 2.01 so this wasn't a big leap. Never hurts to check and be sure.