How can the maximum average power transfer be negative in a power delivery circuit?
If you have an impedance with a negative real part, it delivers power, yes. But remember: no actual passive component has a negative value! To build that negative resistance, you need active circuitry that do consume dc power. The very fact you mentioned (infinite power loop) is the concept behind designing oscillators. They consume dc power to be able to maintain a constant oscillation amplitude. Maximum power transfer is meaningless unless it is defined for a certain scenario. Most discussion about this theorem is made in dc where no negative resistances are possible. In amplifiers, maximum power transfer results in only 50% efficiency and is not always of interest. In Radio Frequency circuits, this theorem translates to impedance matching and reflection reduction. To wrap up, having a negative Thevenin equivalent resistance does result in a theoretical infinite power delivery but you have to keep in mind where that resistance is resulted from and what the circuit aims for.