I want to create a struct that inherits from another struct so it gets put on the stack
You cant:
Structs can implement an interface but they cannot inherit from another struct.
per MSDN
Speed is of high importance
You are assuming that structs are slower than classes. While there may be some speed difference, I would not make this assumption categorically. What you are doing with the clases/structs is very likely to be slower than the memory access.
If inheritance is a key requirement, then you'll need to build your objects as classes rather than structs. Or use another pattern like encapsulation (have one struct be a property of another).
If you get to the point that you can prove that classes will be slower that structs in your scenario, your only option may be to replicate the necessary fields in the structure map.