I don't think it's the marsala as all the brands (good or bad) have the same features and alcoholic content...maybe it's likely you have to get used to your new pan.
In any case, the easiest way to get a well thickened sauce is, simply, leaving the meat scallops into the pan after having added the marsala. You may think that the flour coating could come off the meat, but if you have dredged and cooked correctly the scallops (I mean they must be absolutely dry and the excess of flour must be removed shaking them before cooking) it don't. Only a limited amount of flour will come off the meat, just what you need to thicken the sauce without adding cornstarch or arrowroot, and the "Scaloppine" will end up much tastier.
Of course this way you must cook the shallots before the meat and the mushrooms separately (I don't have this problem as I usually make the Scaloppine plain).
If you use veal meat you must be careful it doesn't overcook: cook it only for few mins before adding the marsala and salt only at the end.
Can I add other 2 cents?
The Piccata and the Scaloppine al Marsala are two of the commonest types of "Scaloppine", a generic name that in Italy indicates all the recipes made with thin meat slices coated with flour and cooked in butter. Other two recipes, very quick and tasty as well, are the:
SCALOPPINE ALLA PIZZAIOLA
Each pound of veal or chicken meat, make a sauce with:
-1 pound chopped fresh tomatoes, or 1 can tomato puree
-1 or 2 garlic cloves, sliced or chopped according to your taste
-1 whole piece of carrot
-1 whole piece of celery stalk
-1 small onion, chopped (optional)
-salt and pepper
Gently fry in oil the vegetables for some mins, add the tomatoes and cook until thick. Remove the carrot and celery.
Dredge the meat in flour and cook in butter for a couple of mins. Turn on the other side, cover the scallops with 2-3 tbsp tomato sauce, sprinkle with minced oregano, cover the pan and cook for other few mins. Place the meat in the dish, pour the reduction on and garnish with black olives or capers if you like.
SCALOPPINE ALLA BOLOGNESE
Make the plain Scaloppine as usual. After having cooked for 2 mins the first side, turn them and put on a single slice of Prosciutto Crudo, then cover with thin leaves of Parmigiano cheese. Cover the pan and cook until the cheese is melted.
If you substitute the Prosciutto Crudo with Prosciutto Cotto and the Parmigiano with Fontina Valdostana cheese, you'll get the SCALOPPINE ALLA VALDOSTANA, that are even better!
This is a "quick" version of the recipe. For the real one, you are supposed to cook completely the Scaloppine, adding some white wine to the reduction; arrange them in a buttered baking dish; cover with the slices of Prosciutto and cheese; pour the reduction on; bake at 350°-380° until the cheese is melted.
The advantage is that you can prepare the dish in advance and bake it just before serving:)
You can also prepare this dish with the Cotolette alla Milanese (dipped in breadcrumbs and fried...suppose you don't need the recipe!) insted of the Scaloppine.
Of course you have to call them "Cotolette alla Bolognese" o "alla Valdostana":) :)