You will have a great time, regardless and I think you have a very small difference of experience almost regardless of your excellent options. I was in the NW for a week this June, we had uncharacteristically wonderful weather with no rain, 75-80 everyday, mild winds (except Siloth). We based ourselves in Southport, at the Vincent Hotel which was just fine.
While we enjoyed Siloth, without a forecaddie in that wind it was not enjoyable as we lost way too many balls. We agreed to play lateral that day, but when you know the ball is like less than 10 feet in and can't find it gets frustrating. I wouldn't do the drive again, but glad we experienced an out of the way gem not talked about nearly as much as the others.
The rota courses are all great. I rank them Lytham, Birkdale, Liverpool. The changes at Birkdale were new and felt that way, needs time for the surface to take root and play like the rest. I just find Lytham a wonderful mix of shots, with protected holes, wide open holes, short and long (especially into winds). While basing oneself in one place helps for a relaxing trip, I would have liked to stay in the dormy house there one night.
Formby was outstanding and unlike any of the others, with trees on a links. Pleasantly surprised as I didn't expect that so close to the ocean, unique in England even.
Outside of those four or five (depending on adding Siloth) I don't have strong feelings one way or another. You will have a great time, there will be variety and you will get to appreciate that variety on the 3 open venues even as Liverpool is flat and right in front of you, with Birkdale being rugged, Lytham a mix. Enjoy it you will.