I can only give you a qualitative answer based on my experience. But I'm doing a lot of Europium based chemistry where I use Europium metal as reagent, often together with sodium as a fluxing agent. The sodium is then removed using liquid ammonia by constantly dissolving it, decanting it off and warming it up.
Just to give you an idea, I'm using about 90 - 100 mg of Sodium metal usually. My container is filled with, I'd say about 10-15 ml ammonia per run. It will take me about 20-25 repetitions until I have most of the Sodium removed, which is about 1-2h of work. And that is just for the Sodium. If we use Lithium it will take much longer. And I usually find metals like Sr, Ba, Sm or Yb still in my washed sample.
If you have traces of other metals present, say Eu or Sr the removed sodium will often adopt a golden color. So it's usually a mixture and not well separated, just as you assumed it. But I imagine you could perhaps dissolve the Magnesium and separate it from other metals that way. But using standard pressure would most likely take forever. I never tried Magnesium but I can tell about Sodium, Lithium, Strontium, and Europium. And the latter ones are extremely slow.
This could perhaps be increased if you left the metal for a while in the ammonia or if the pressure or temperature is increased.
Our setup works by cooling down the vessel to - 80°C so the ammonia will liquify. And then immediately pour it off to save time. So there isn't much time for the metals to dissolve and the pressure is then often at around 350 - 400 mbars.
But as I said this is just from my experience, a specially designed setup may work in your case.