Two other thoughts. Re-examining the dialogue from "Balance of Terror" I couldn't help the feeling that the Romulan attack and testing mission was somewhat reminiscent of Dolittle's B-29 Tokyo raid in WWII where they discarded everything expendable to lower their weight.
In one scene the Romulan Commander inquires whether they still have some old style nuclear warheads on board. Shouldn't he know what they have on board or not?
As for "The Enterprise Incident" we learn that the mission is to acquire a Romulan cloaking device or maybe more specific the operating device. Theoretically the Enterprise could have been upgraded with the technology to produce a cloaking effect prior to the mission but still lacks one vital component - the cloaking device.
In essence all Scotty had to do is install the device and throw the switch - which is basically what he did and all his usual lamentations (did Kirk sound bored on the Bridge?!) were just for drama...