FYI- I'd play Belvedere or The Mines over Arcadia irrespective of price.
I haven't played Belvedere so won't comment on that. But I'd ask the basis of your preference of the Mines over Arcadia -- is it the architecture, or is it that the Mines is more suited to your game? If the latter, I have no issue with playability as a driver of preference, but I question when personal preference is confused with the a priori "goodness" of a course's design.
I have played Arcadia a dozen or so times and think that it is a very good course. In that area, Crystal Downs and Kingsley (disclaimer: I am a member) are clearly better. But Arcadia offers some interesting holes (8 and 12 are two I particularly like) and presents a number of things the hypothetical Ideal GCA'er is supposed to like but, in the case of Arcadia, are quickly dismissed due to the fact that it has a nice veranda and is swarmed by "retail golfers." I also find some of the criticisms frequently levied puzzling and/or a bit unfair.
For example:
Firm/fast playing conditions -- In my dozen or so plays, Arcadia has been exceptionally firm and fast, which is something I thought GCA'ers liked.
Bold greens -- Massive contours that cause the player to think about approach shots, recoveries and putts? Check. I find the recurring criticism that the greens are too bold comical, especially given the praise we collectively bestow on places like Yale.
Mounding / manufactured feel -- Yes, it can feel a bit goofy to play through valleys of tall dunes on flatt-ish fairways. But don't a number of courses in GB&I follow similar approaches? And does anybody really think that the Mac-Raynors don't feel "manufactured"?
Walkability / routing -- It isn't the easiest terrain and there are some hefty distances from green to tee in a few places, but it is very doable, especially with a caddie -- and don't GCA'ers support caddie programs? I'd put it on par with Whistling Straits and Erin Hills in terms of both terrain and distance.
The setting -- Many people will comment on the view and pleasantries of drinks on the porch before discussing the course. But so what?
For those who haven't played it, I would always recommend a round. Sure, you might not like it. But that can the true with any new course and, in this case, at least you'll be able to articulate a reason for said dislike other than the fact that a guy who disses Coldplay and thus must have finely tuned sensibilities
says so.