Thank you, that all sounds right. I've been looking for, perhaps not a single engine, but rather specialized libraries I could glue together that handle different aspects of the problem. Sounds like I'll have to roll my own from scratch.
Can you recommend any general-purpose libraries (preferably with python bindings) for tensor calculus?
My understanding is the numerical GR community is moving in this direction. The theory people tend to roll their own inside of Mathematica or Maple. Some Maple users use GRTensorIII (https://github.com/grtensor/grtensor)
Can you recommend any general-purpose libraries (preferably with python bindings) for tensor calculus?