I'm tending to think that your second option, in restricting what you're hearing to being "Left channel only" from the Roland, may not adversely affect some sounds, but will DEFINITELY reduce the ambience and depth of others.
I'd also like to offer yet another option for you to consider...
...and that's using a pair of custom TRS to RCA cables that would allow your Quad-Capture to come into the L3t's "Aux" Inputs.
They'd need to have NO sleeve (Outer "Gnd" or "Earth" shield connection, often braided) wired to those RCA plugs, with just their internal "hot" or "tip" conductor going to the central pins of the RCA plugs and the internal "cold" or "ring" conductor going to the RCA plugs' outer "skirt" contacts.
(You could also try achieving the same hook-up via "off the shelf" guitar jack plug to RCA adapter cables by dint of using the Roland's "Ground Lift" switch to get rid of any hum that's likely to ensue.)
To my mind, connecting your Quad-Capture to the "Aux" inputs could allow you maximum flexibility of experimentation with (and choice from) a staggering variety of practice, recording and performance configurations, whereby that amazingly powerful mixer you've bought in your L3t could possibly become something of a "control hub" for your entire Marshall, Mesa-Boogie and Roland rig ...and/ or simply be used on its own.
As for your L3t standing vertically or lying on its side, I'd have thought that the "best practice" is simply the one that suits YOU best, as its inbuilt mini gyro system will automatically "tailor" the response of your L3t to match its orientation.