That is a pretty impressive list even if Hoylake isn't there.
West Lancs is quite austere. It's at the southern end of that stretch of dunes ending in Southport. It's a good course, though, and the challenge is considerable. It's not visually memorable, but I am sure you'll enjoy it.
Hillside doesn't get a great reaction on this site, but I love it. The flatter holes on the front nine are similar to those of S & A separeted from it only by a railway line. The (newer) back nine explores mountainous dunes overlooking Royal Birkdale. I find these holes very enjoyable. Others complain about a lack of width.
Royal Birkdale also comes in for criticism on GCA, largely because of the way its fairways are routed along the valleys through the dunes, creating lovely flat lies, far removed from the traditional links. OK, it's not Royal County Down or Sandwich in that respect, but you still have to hit the fairways and there are some pretty effective defences if you don't get it right. There are many very good holes, perhaps no great ones, but it's a good test of golf and the greens are deceptively tricky to putt. The clubhouse is very comfortable - not at all intimidating as some Open Championship clubhouses are.
I love Formby. It's such an interesting course and I adore the new holes through the pine forest. Look out for red squirrels, an endangered species in the UK. Have a look at Sean Arble's recent posting on the course.
Wallasey has some impressive dunes and it exploits them well. There are some great green sites and many an inspiring view from the tee. There are also some flat holes, which some like less. To my taste these are also good holes - I also like the flat holes at Aberdovey and Harlech.
Royal Lytham - flat as a pancake, surrounded by housing and a railway line, with no sight of the sea. But what a difficult course! Does it have more bunkers than any other Open venue? After the first tee shot you are rivetted - you never notice the housing or railway - and you find that, like Hoyake, there are more undulations than you imagine, viewing the course for the first time.
Southport and Ainsdale is to my mind the least attractive of the courses, but it is an ex-Ryder Cup venue (a rare GB and I win). It's quirky and there are some fairly ordinary holes at the far end of the course, but it's no slouch.
I think this has the potential to be a pretty exhaustive test of golfing ability with the added benefit of minimal travelling once you get there. I'm sure you'll enjoy it.