To expand a bit on Ronin...this is a situation where a suitable mixer is pretty essential. Instead of looking at them as a way to combine audio together, look at a performance mixer as a control point where you have several "instrument" patches like the above already prepatched and ready to shift from one to another by bringing channels in and out. This avoids your having to repatch constantly, makes the above concept work for both studio AND live.
However, I have some concerns about the size of the build. To get the above idea to work really well, you'll need to have space for a proper performance mixer, for a few extra modules (notably attenuverters...you can wring a lot of control power out of 'em, even if they're boring and unsexy) to assist in controlling activity in the subpatches, logic and timing modules to complicate the trigger/gate situation, and so on. It's an ambitious idea...but the fact is that 2 x 104 cabs are easy to get and cheap (often as cheap as some higher-end 1 x 104s), or you can add a bit more potential with a 7U cab that gives you some tiles and, potentially, cab integration if you go with Intellijel's 7U 104 hp case.
One last warning...don't think you'll be able to send the Moog's line output back into the Eurorack mixer directly, because you likely won't get a usable result due to the major voltage differences. It either has to be preamped first...or just don't do that, and mix it as per usual along with the modular on a typical small mixer. The latter is cheaper, fyi.