That was pretty much the same experience I had in doing a power supply in another project I was working on. The plastic three legged regulators were rated at 1 amp and only with a heat sink. The project drew 950 ma and even with a good heat sink, it would start shutting down. I went to a TO5 case regulator with a 3 Amp rating, problem solved. Unfortunately, they stopped making those years ago.
As a result, I did not even think about using one in the 'Cuda and went with the RTE.
Craig