Is inverse quantum confinement possible? In the "Particle in a Box" thought experiment/analogy, the reduction in volume of a cavity enclosing a particle will lead to an increase in the bandgaps energy levels that simulate that of an atom. A reduction in size means an increase the photon energy emitted/absorbed.  This matches the observation on semiconducting quantum dots of various materials, proving its validity.
Yet in a class of global aromatic molecules, known as Cycloparaphenylene's the opposite occurs. An increase in size leads to an increase in energy. This seems contrary to the postulate in the first paragraph. Is there another mechanism at work or can this still be explained by the previous framework somehow?
This is the research article were the diagram is from. There is nothing on the nature of the fluorescence, just the synthesis steps, but I'm including it either way: Selective Synthesis of Strained [7]Cycloparaphenylene: An Orange-Emitting Fluorophore



 A: 
In the "Particle in a Box" thought experiment/analogy, the reduction in volume of a cavity enclosing a particle will lead to an increase in the bandgaps energy levels that simulate that ofan atom.


Yet in a class of global aromatic molecules, known as Cycloparaphenylenes the opposite occurs. (Emphasis added.)

No. This is not what is happening. The length scale you are illustrating is not the correct length scale to consider. The electrons are not "filling in the donut hole" in any meaningful way. For the most part the electrons are going to "want" to stay near the atomic cores.
If the 1.6nm length scale ("donut diameter") was the appropriate length scale to consider, then your simple model (Particle-in-a-box) would predict photon wavelengths of around 82656 nm. This is not the photon wavelength you are considering, so clearly this is the wrong way to model the system/process.
What is potentially happening is the that increase in the overall size of the "donut" may decrease the size of other relevant parameters such as the spacing between some of the individual atoms in the molecule.
