You are correct - you train for the A340, you only fly the A340. but like any otehr license, you need to convert if you want to fly another aircraft.
The whole point of the MPL is to get you into the RHS of an airliner in 12 months so of course - it will only be on that aircraft. And just like an ATPL, if your type rated on a 340, you can't go and fly on a 737! We know this.
I've done some further research and it seems that the MPL has even more limitations. For example, you learn the SOP of the airline (if the school is afiliated with an airline) or the SOP of the aircraft your training on. So perhaps I was wrong to assume that the pilot with a Type rating has a greater advantage than one with an ATPL.
At the end of the day, the airline you join may have its own SOP so you have to go on this course anyway - regardless of your experience on type.
I dunno. its a tough one.