12 x 52 is the right tank size. A 12 x 48 is undersized but only by the smallest amount and from a real world perspective, it would probably not matter unless your water was cold and you did not have a top screen. I have charts at the shop that show exact capacities including dome information. The actual part of the tank that is supposed to be considered for the resin or media capacity is the seam to seam measurement, not the total tank. The domes are not used in calculating a tanks media capacity. If I remember correctly, the 12x52 has a media capacity excluding domes of 2.1 cu. ft assuming a 50% freeboard. So a 12 x 48 would probably be around 1.75... this is all technical jargon that should be used by the designers.
So... to make it simple, the 12x52 is the correct tank, but if someone uses a 12x48, I am not going to complain. The 5600SXT or the 7000SXT will both do you just fine for your application. The 7000SXT is a much more modern valve that is much simpler than the 5600SXT, but either valve will last you a very long time with very little trouble.
While I am not personally a huge fan of the Vortech tank design, it is primarily because when a problem does occur, it comes back to me for repairs or replacement. This is not an issue with a standard design as long as a very good quality bottom screen is used. I only use the 40922 or 40924 bottom screen from Pentair. It cost 10X more than a junk bottom screen, but this is a very critical part of the system and any company that tries to save literally $3 here is a company I would avoid. Clack also make a heavy bottom screen that is almost as good.
If you go with a standard tank design instead of the vortech, definetly go with the 32mm distributor. I am not aware of any junk screens being made in that size, only the Pentair and Clack versions are readily available. Considering the 7000XT only costs a few dollars more, there is no negative to the larger valve or manifold.