I would definitly try brewing it without the milk first. not only is it cooling down your brewing water but it is going to change the way the tea brews.
Twinings is not exactly the mercedes of English Breakfast teas but if you liked it before with your old difuser then why switch to another one? [my fave jasmine tea is 99 cents a box at my fave take out place so I'm not one to judge honestly ] The kind of difuser you're describing as your new one would be a 'better' difuser but if it's not making you a better cup I say pitch it [or put it in the cupboard] in favor of the old one! Who cares if it tastes good