Dead right there, RR/Allison are quite specific in mandating against "venting" their engines after shut down, citing thermal shock damage as a likely consequence. Conversely, the LT101 is required to be motored for 10 seconds after shut down, to move the oil around and prevent coking in the oil galleries
Also, the practice of cross starting is allowed by some manufacturers, and not by others. It can put a strain on the starter/gen quill shaft, leading to failure, when the extra load is applied during cross start. Watch the ammeter load go off the clock, and consider the effect it might be having!
C4's reply is as good as you'll get.