heh, lets look at things one by one, starting with
In order to have a device with at least 2 input and 1 output, from manufacturer design, it involved mixing signal. If not, theres no point in having a product with 2 in(or more) and 1 out.
With the first thing you mentioned, for versatility sake, if needing either 2 in and 1 out or vice versa, theres passive mixer device which can mix 4 in and 1 out. The good thing is that such device, when the volume knobs on it are all turn up to maximum, it will reverse the input and output, to 1 in and 4 out. An example of such mixer is from rolls(
http://www.rolls.com/), which can be gotten from sim lim square, hung bros.
Hehe, world aint perfect unfortunately, since its a passive mixer and not meant for instrument signal like our geetar, it will have issue of phase and impedance mismatch which make geetar sound dull and lifeless(when combining multiple instrument). I have tried this myself, the sound is just dead.
As you mentioned earlier, you dont wanna combine signal, but wanna 2 different groups of effect to go into same amp. So for that, do you want to have 2 different group of effect output into the amp at the same time or at any point, only 1 group of effect output going into the amp?
One last thing, are you familiar with effect looper send/return?
heh, just wanna clarify before going further, got a feeling that thats some missing link on the understanding of guitar signal input path to pedalboard 1 and 2, pedalboard output path(Loop send/return) to amp. Oh, not sure if check out the spec for boss ls 2, if have can use that as example of what it couldnt achieve for what you wanna do. It will be easier.