Sounds like you need a patch bay to me.
If you add a mixer to the chain, its going to bottleneck the signal with whatever fidelity losses it produces.
You'll then be using three preamps in series, the mixer, the 1073, and the interface preamps before it gets digitized.
If your problem is a lack of inputs running multiple pieces of gear, don't waste money on a mixer. Its completely redundant and can only add hiss and noise to the signal chain. (and any frequency losses) if you use a patch bay it will minimize your cable swapping issues. Wire all your gear to the back of the patch bay then use jumpers in front to swap your inputs and outputs. So lone as things are properly labeled its a no brainer and can be done using 1 hand.
I wouldn't spend any more then needed for a patch bay either. A low cost Behringer or Samson use the exact same jacks as your higer end patch bays with the exception of some custom made pro stuff that use vintage metal type telephone jacks.
The other thing to think about is investing in an interface that has more inputs. If you have 4 stereo keyboards, an 8 channel interface will allow you to keep the gear connected with no need to swap wires. You can actually swap keyboards or play more then one at a time during s single session and have them all come out on separate stereo tracks. Like many I started off using a windows sound card them moved to using a pro card then a 4/8/16/24 track card. I haven't had to swap cables in the studio is years. The most I may do is insert a piece of gear in the front end and that's simply a matter of moving a couple of jumpers on the patch bay.
In short you pay for convenience. A mixer is not nessasary at all. Even if you have hardware you want to run I'd still suggest a multi channel interface and patch bay. Something like the Tascam 16x08 allows you to record 16 channels at once, 8 mic inputs and 8 TRS line inputs You could run preamps into those TRS or keyboards, or loop any effects you want in and out and set up aux busses in the DAW itself which loop the channels through hardware effects. You used to need a hardware mixer recording to tape. It was an essential piece of gear for reamplifying and mixing. Recording digital, its a redundant piece of gear.
Back when I first switched to recording gear I thought the best method would be to use my mixer the same way as I did recording to tape. The Soundcraftsman mixer I used back then wasn't bad either. I got some amazing analog recordings using it. Within a week I was making audio comparisons recording with and without the mixer and there was no doubt, the fidelity was higher quality with a much lower noise floor recording direct without all that additional hardware.
In short the shortest path is the truest. Anything you put in series will bottleneck the signals and bring it down to the lowest quality components. If the quality of the gear is better then what you have in the interface, (like those 1073 preamps might be) then the gear may be transparent and only add whatever ambient noise and distortion every piece of gear adds.
Of course there are no rules on using gear to color the sound with its quality if you want. If I had a unique console that does amazing things, there is no doubt I'd find a way to incorporate that into my signal chain. There aren't many budget mixers which will substitute doing that job, especially PA mixers. PA mixers are designed to make mics loud and EQ's are chosen to minimize feedback in a live venue. Most are complete garbage for recording purposes.
If you wanted to combine a mixer and digital, your best solutions are a digital mixer. Presonus, Zoom Rolland, Tascam, Peavey and others make some excellent units. I've hears some live recording made on them which knocked my socks off. I'd have a hard time matching what I heard using state of the art analog. The nice part is they double as a recording or live mixer so its one less piece of gear you need to buy. Its also perfectly suited for both jobs. The quality of the sound effects in some of them is excellent too. Of course the price tag is what hurts but they are coming down all the time. What cost $2500 a few years ago is only $600 today so you need to keep that in perspective.
Some time soon I wouldn't mind selling off all my Passive PA gear. Cabs, Power amps, Rack effects, Mixers etc and buy a digital mixer and a good set of powered speakers. Life would be so much easier playing live without needing an entire road crew to haul and do setups. Best part I can record live or studio.