. . . I am wondering about how EMD engine models overlapped. In particular, the GP7 and the GP20 . . . what about hauling goods on the rails? Did the folks who had the older models immediately try to trade up for the better performance? . . .
No.
By the time the GP20 was offered, GP7 and GP9 units were too new for trade-in unless they were badly wrecked. First generation diesels were financially amortized over a 15 year period, and that's why you saw FT, F2, F3, Alco and Fairbanks-Morse locomotives often being retired after 15 years of service. GP7's and GP9's are the "Energizer Bunnies" of the locomotive world; they kept going, and going, and going, long past their 15-year amortization. Many went through capital rebuilding (and another 15-year amortization) and lots of them remained in service, supplanted on the main line hotshots by higher horsepower units, but still slugging away in secondary freight service as well as yard service. I can't think of any that were offered as trade-ins, though hundreds have been re-sold through used locomotive dealers after as much as 50 years of service..
In the late 1950's EMD offered an attractive trade-in of FT units, first on GP9's starting around 1956, and then on through GP18, GP20, GP30, and GP35 units, which resulted in the disappearance of almost all FT units. Locomotives are too expensive to trade in or retire in less than 15 years, except in the case of a very few models that were so problematic that they were too costly to continue using.
Would you find lash-ups made this way? Could they be made this way?
Yes.
By the time that the GP20 was produced, railroads had standardized on a single 27-pin jumper cable for multiple unit control*. This allowed multiple unit operation with other post-1945 EMD's and (eventually) most locomotives from Alco and GE. FT's and early postwar Alcos used a different number/arrangement of pins, but this was changed by almost all railroads to the 27-pin standard m-u arrangement by the middle 1950's.
* The exception [applicable only for first generation EMD units equipped with dynamic brake] which lasted until the GP20 and then ended, was the EMD field loop cable for dynamic brake control. This cable was fitted into a rectangular receptacle usually located above the round Multiple unit jumper cable receptacle. EMD dynamic braking equipped units needed the field loop to control or to be controlled by other units only when in dynamic braking. Most railroads converted their field loop-equipped locomotives so they could use the "more modern" potential line control for dynamic braking. Not SP, though. They ordered locomotives up through SD45's with field loop receptacles and a selector switch for the Engineer to use field loop when m-ued with SP's huge number of unmodified SD9's and GP9's, or to use potential line control when no field loop units were in the locomotive consist.
Also, Union Pacific used a 3-cable multiple unit arrangement up through the mid-to late 1950's. UP and Northern Pacific had a few sets of really odd jumper cables, to m-u GP9's of both railroads when they operated together on the Camas Prairie Railroad in Idaho, which was jointly owned by Union Pacific and Northern Pacific.