What regular product can replace Philadelphia cooking creme in a chicken pie recipe?

Why not make your own cheese sauce. You could do something like; roux, milk and cheese.

Or you could always use something like ricotta cheese or boursin cheese that is a spreadable and more natural cheese.

You could try mixing some (tbs or two) cornflour with a little water to make a paste, stir that through some thickened cream (250/300ml?), mix in some dried or fresh herbs of choice then stir that together with your chicken and veg mixture till it just starts to thicken. I would also add a good amount of fresh pepper and some cheese, otherwise it is going to be very bland indeed. Bake as directed in recipe.

If you want the garlic flavour you should fry it at the same time as the chicken, or maybe use garlic powder or garlic infused oil. Incidentally, if it is simplicity you are after you could further amend this dish to use a pre-cooked chicken or leftovers and forego the saucepans altogether.

I've never used the stuff, but posts online suggest that you can thin cream cheese (8oz cream cheese + 1/2c chicken broth).

Other alternatives might be a yogurt or Mexican crema.

You'll also need to adjust salt and other seasonings.

I make pies like this quite often and I use white wine and double cream as the liquid. I put 200ml or so of wine which I bubble down till it's about half or a bit less then add 300ml or so of double cream (and usually mustard and tarragon) and bubble slowly into it thickens. Usually it's thick enough like this to make a delicious creamy filling, but sometimes I need to reduce a little.

Honestly though the idea of using frozen defrosted veg is the thing that puts me off that recipe. I'd just soften some onions, carrots and celery in butter, add the browned chicken (and some halved mushrooms), then add the wine and cream.

YMMV.