The 1966 C10 came standard with two stage rear coil springs. Similar to your first picture. An optional higher load rating was available but was also two stage. The only single stage, similar to your second picture, came on panels, not suburban. Don't know where/who you got the single stage spring from or what year truck? I assume the difference in the two, two stage coils available for your Burb are "wire diameter" which is one of the factors that determines spring rate. You will have to study up to find out how to tell one from the other and if you actually have the optional "heavy duty". While your springs do look stock, I do not think they should be touching without load. The center coils do touch first however. This seems to be introduced in 1963. Some folks call the two stage, "progressive". If you find a donor pair of two stage, standard duty that are not touching, they will ride just fine. The two stage you show are on "heavy duty" all the time.
Another option was a leaf spring helper in rear.