Fascinating question. Cutting those 3 bikes down to 2 should be possible. Whether it is desirable, of course, is another matter.
The obvious solution is to find something that sits between the trail bike and the XC bike i.e. a bit more fun than the XC bike and a bit faster than the trail bike, but I’m not sure that’s really what you are after. You mention that the trail bike “isn’t fun enough for the compromise in efficiency”. I think the problem here is that your reference point for fun is the DH bike and I wonder whether you’ll ever like a bike that is less fun than that.
So, I’d be tempted to forget the XC stuff and try to find something that is as much fun as the DH bike but efficient enough that you can ride it all day on XC trails.
I think you are on the right track with the big wheelers (to get a bit more XC efficiency), but suspect that you might need a properly slack and long bike to tick the fun boxes.
It might be worth considering an “all mountain” 29er (like the Alpine Five, Codeine etc). They should be a lot of fun on the way down, but still faster than your DH bike everywhere else.
A shorter travel version of these that retains the same hooligan angles could be an even better fit, but there are very few of these around. Most manufacturers seem to be nervous about making a properly slack short travel 29er. Maybe for good reasons, I don’t know.
The Orange Segment seems to have been designed for what you want, but since nobody has ridden one I guess that nobody can say whether it hits the mark or not. Wont stop some folk slagging it off though:-)
The new Works SCR version of the Whyte T129 might also be worth a look, but probably still a bit to XC focused for your needs.
Banshee Phantom looks close as does the Process 111 and I would have thought that Nicolai would do something that fitted to bill too.
Anyway, good luck. I look forward to hearing what you choose and how you get on with it.