Hadn't thought about a CloudWatch even to keep the function warm, I might suggest that to the team.
We haven't shrunk the model, we've deleted superfluous files from the TensorFlow python library and dependencies (we don't need tensorboard, for example).
It would be nice if you could package TensorFlow up into a minimal component just for assessment and not have any of the 'learning' stuff or other added-on libraries, but we couldn't find a simple way of doing that - we're not pro C++ engineers and even our python is not the greatest. We're managing for now, but if our model grows any bigger we will run into issues, but there have been some good suggestions in here.
We had considered the S3 store, but we ruled that out quite quickly for cost & performance at the number of invocations a months we're looking at - but that was before we knew more about the 'keeping warm', so that may be revisited, too.