There's a couple limitations on the setup that have me puzzled. The Katana does not have a direct out, but a headphones/line out, so you can't record that direct without shutting off the speaker. Of course, it and the drums are probably so loud the mic recording will be primarily those. If you don't have a PA, how does anyone hear a vocal, or is it just instrumentals? Similar problem about the direct recording of the digital piano. I'm assuming (hoping) it has a separate line out, and not limited to a headphone/line like the Katana, because then your options get a bit more limited. And, is there a bass? I didn't read that in the OP, or is it also getting plugged into the Katana?
The H6 will allow you to control the headphone/monitor mix independently of the record levels, so you can control what goes to the camera that way, but you'll have to watch levels closely.
I'm kind of siding with the small PA contingent here because it can give you a place to plug in the keys, even a bass and vocal mic, and you can take that "live" mix to your DSLR. Much as I liked my H6, it's fairly limited, based on the few years I used mine. As others suggested, the used market has lots of options for mixers, and there are inexpensive powered speakers, even 1 speaker, that would elevate the sound of the keys/bass/whatever.