Document multiple "If this field is empty" fields

That sounds like it would be far more work to put into the module (and risk breaking other stuff), than it would be to just fix on your site. My suggestion is this:
1) Add in all of the views fields you want to check, and make them hidden (exclude from display)
2) Add an empty views field as a placeholder for the final display you want
3) Create a template file to override the view (check the theming information link on your view)

Then, you can simply put some simple php logic in your template file to check for which fields are empty or not. This could be a few if statements, or even a switch/case statement. The specifics will depend upon your use case.

I realize that you may not consider yourself a coder, but as scary as this may sound, its really pretty straightforward... and you will get your solution much faster than waiting to see if/when the module maintainer can get to a more complex solution.

If you post on the general forum (or IRC), then you can get specific help as you need it and as determined by your specific case.

If all else fails, you can post a bounty on the forum which can get you a quick solution too. This should be pretty cheap as its pretty simple, and you may want to spend a few bucks instead of learning how to do it yourself.

You can actually do this by daisy-chaining multiple ifempty fields together. I did this in a POC for a client yesterday and it worked just fine. :-) I suggest adding a bit of documentation to the project page and the readme describing this. The second ifempty field uses the first one for it's first value and your extra fallback field for its second one. Presumably you could do that as many times as you needed, but I don't know how performant it'd be (and it's a bit slow to set up).

I have reworked the project page to add a Frequently Asked Questions section, and I've included this question at the end. @seanr, thanks for your assist with this!