Regarding the 7000SXT, you will not be dissapointed. This is an old debate that is silly. Only one guy on this site does not like it, and his reaoning is because it is too hard to work on, and he personally had problems all the time with them. Funny, because it is the most reliable control we distribute. We distribute, Clack, Autotrol, Pentair, and many others. You are correct on the 5600 only handling Cation softener tanks as large as 12", the 7000 can handle the 13 or 14" tank you need. You could use the 2.5 Cu, Ft system, and the system size will be much smaller. The 3 cu. ft. unit is technically supposed to be spec'd out with a 14" x 65" tank. The 13 x 54 that is used for the 2.5 is a lot smaller and it puts the control valve right in front of your face. I would also recommend not using a low salt setting ever when using cation resin for iron removal, use a minimum of 8 pounds per cu. ft, you will lose a very small amount of efficiency, but it will assist the resin from becoming fouled.
You could also use the Clack Res-Up chemical feeder to help keep the resin clean, it is cheap, reliable, and simple.