Well, I'm prepared to have another go! I made cheese straws last week from a different recipe, and the straws were good, but just not cheesy enough. I had used gruyere and grana padano cheeses. Yesterday I got another roll of pastry and a block of extra mature cheddar. I have French's American mustard. Now normally I, weirdly, never eat mustard! Only when I make a hotdog with a genuine German Bockwurst do I add a little mustard. But, okay, you said there is no overpowering taste of mustard when the straws are cooked, so I'm going to use some. I'll edit this comment in a few days' time once I've made them.
American mustard is very mild and would not help the flavour. Just use extra mature cheddar cheese and go without the mustard if you do not have English Mustard. Parmesan cheese on top will also add to the ‘cheesy’ flavour