Offered FWIW: I was at a cooking demo a few months back, and during the Q&A session after, someone asked about the key to successful veal (or chicken) marsala. His response was to use lots of butter, and to cook "low and slow," as others have suggested, so as not to "break" the butter. If you try to hurry things up, he said, you end up with a dish that doesn't taste right.
Now, he did not give proportions for his version, so I don't know how much butter he meant, but in reviewing the recipe you posted, the method and butter quantity seems diametrically opposed to what this chef recommended (sorry, can't remember his name!).
So, I guess my suggestion would be to maybe search for additional recipes and settle on one (or adapt one) that suits.
Good luck, and let us know how your next version turns out!
"When I'm born I'm a Tar Heel bred, and when I die I'm a Tar Heel dead."