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Need help on two over one responses in big club context

My partner (Kees) and I have been playing a Big Club system loosely based on Viking Precision for about 20 years. We're currently restructuring some of the (non-GF) crud that has been part of our system for ages, both for optimization purposes as well as mitigating the memory strain. We're on the fence about how to effectively handle two over one responses to our 1M openings, though.

To add some constraints:

  • 1M - 1NT: GF relay
  • 1M - 2M-1: good raise or better for partner's M
  • 1M - 3m: Natural invite (6+)

The first constraint is non-negotiable system wise, the latter ones would be nice to see included. Is there a viable approach that would let us sign off as cheaply as possible in responder's suit and combine it with a variety of invitational hands? 

Would you share your notes/suggestions/ideas with us, please?

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