The universe does indeed exist when it is not being observed

Perhaps the observed less than zero photons does actually point to a distinction among photon antiphoton pairs which is an anathema among quantum-electro-dynamicists. A distinction between photons and any real antiparticles would perhaps be just as weird as the concept of less than zero photons occupying a given region of space. Perhaps the lack of even zero photons is nature's proxy for negative electromagnetic energy and so the paradox is somehow resolved in consideration of the vacuum energy state of the region where there was a reported less than zero number of photons.

An analogous situation is the presence of electron holes within semiconductors wherein when a electron leaves a region within a differential volumetric element of a neutral piece of semiconductor, a charge vacancy is left in its place with less than zero or less than neutral negative electrical charge in the form of an electron hole. These holes act like positively electrically charged particles and behave as if the have a psuedomass. The working concept of electrons and electron holes in semiconductors is a well established convention of solid state physicists and electrical engineers as they develop new semiconducting devices and materials.

Another possibility is that sets can contain numbers of elements that have a number of elements of less than zero elements. The idea here is that the absolute value of the number of photons observed in the region where less than zero photons was observed is equal to a freaky value of less than zero but wherein this value is neither negative nor imaginary.