With a fractional rig, the windward runner is used to tension the headstay. Although primarily for upwind control of foresail shape, it will also stabilize the rig off the wind - particularly when flying a standard spinnaker. They don't do much for a big masthead chute. A lot of this depends on how sensitive the rig is - carbon fiber? how many spreaders? Some of those CF rigs are very intolerant of crew mistakes.
Masthead rigs are another story. As a rule, the mast stays straight and the backstay tensions the headstay. Sounds like yours are to stabilize the rig and tension the inner forestay. My only concern would be that the inner forestay and the backstay have similar stretch characteristics. If I were you, I'd be interested in knowing if I could use the inner forestay to bend the mast a bit and flatten the main. Might give you another sail control tool. If you try this, stabilize with the runner.