I shoot my Widows, Morrisons, Robertsons & Bob Lee recurves all with the same Rick Welch anchor you describe. There are subtle differences among them, but nothing so dramatic as you describe. I do notice with the Widow that I shoot it better with maybe a 5 degree cant rather than straight up and down, which also brings the point of impact over to the right a little.
You say you get your nose to "lay on top of the fletch." I was taught by Rick to place the tip of my nose behind the cock feather, so that as I draw the bow, the back of the cock feather contacts the tip of my nose. Perhaps that's what you mean, but if not, maybe you could explain.
I find that Rick's method doesn't work (things don't fit) unless I hold my head up. It is probably a good thing that I have something to remind me that my head is drooping. Some archery coaches describe the proper head posture as an "aristocratic look" as if you're looking down your nose more than non-aristocrats usually do.
I'm sorry I can't help you more than this, but I can tell you that I have shot a number of bows, including longbows with straight grips, and find that with very minor adjustments I can use Rick's method of anchoring.
BTW, you didn't mention whether your new Widow is a recurve or a longbow.