Is there anyone knowledgable enough in this area who would be able to comment on some of the possible theoretical/ hypothetical implications of the existence of spin 3 particles? Is there any thought that their existence could imply additional fundamental forces?
If you look at the presentation linked in the link you gave , in page five, you will see that spin 3 resonances have appeared in the charmed section. This is the first indication of similar spectroscopy in the beauty sector. The spin is a combination of quark spins and the angular momentum of the quarks within the resonance.
It is all about how the quarks bind into resonances which is mainly QCD though QED cannot be ignored in the modeling . The study of this spectroscopy will be useful in evaluating QCD phenomenological models. The fundamental forces still are strong, weak, electromagnetic and gravitional.