Skyripper used polypropylene as one of their fuel options for 38mm. The other option was PVC if I remember correctly. The PP gave better performance. Using recycled plastic could be a good option since most recycling plants can hardly give the stuff away.
In fireworking, various synthetics are used for star compositions for mines and aerial shells, including natural and synthetic polymers, as both binders and fuels. But not really for propellant fuels beyond the composite formulations you're already familiar with.
PVC powder, for example, is useful as a slow-medium burn rate fuel that also provides the chlorine necessary for amplifying color saturation needed in most colored comps, and it also acts as a good binder to keep individual stars intact when the aerial burst charge goes off. But PVC has not been explored much as a propellant (in fireworking, at least) because of its not-so-energetic burn when combined with the majority of pyro oxidizers (AP included). Another synthetic plastic-like polymer commonly used (and probably the binder in more than half of commercial aerial fireworks from China because it's so cheap) is phenolic resin, of which there are probably thousands of permutations. Phenolic resins, actually phenol-formaldehyde polymers, were the first true synthetic plastics (e.g., Bakelite). Given there's so many possible types, perhaps one or another might prove to be a useful propellant fuel. Phenol. Formaldehyde. Doesn't exactly ring of environmental friendliness, though....
Other synthetic binders/fuel/chlorine donors in fireworking don't stand out as potential propellant champions because of their mediocre burn rates and energy content. Commonly used synthetics: Parlon,
i.e., chlorinated rubber; original Saran,
i.e. polyvinylidene chloride, Chlorowax,
i.e., chlorinated paraffin--70% chlorine, actually; are all used as combo fuels/chlorine donors in fireworking. But they burn pretty slowly and with variably nasty combustion products. Incidentally, the chlorine that fireworkers love about the original Saran was changed in the early 2000s to polyethylene by SC Johnson, due to the chlorine content and related environmental concerns. Lost a lot of sales with their mutated Saran Wrap. A little off-topic from rocket fuels, but a brief summary of the utility, and generally mediocre and dirty burning characteristics, of many synthetic polymers, even when mixed with hot oxidizers like AP and perc... That said, rocketeers are constantly striving for better propellants, whereas in fireworking, the primary use of rocket propellants (largely restricted to inexpensive BP, whistle, strobe, and some sugar fuels) is A) to launch a pretty device to an appropriate and safe altitude, and B) for the propellant effect itself (strobe/whistle fuels). So there's not really a ton of experimentation in that hobby, outside of select groups, in developing novel propellants based on synthetics. Some, but not much.
Given it's ubiquity across all layers of the globe, it'd be nice to find a true utility for all plastic waste, be it rocket fuel or something else. Although some innovation and creativity has been used to address the plastic "problem", reuse/recycling efforts remain woefully inadequate.
That "trash rocket" in tfish's post above exemplifies the filth of many burning synthetics. There's always room for improvement. His free-burning chunks ignited approximately as vigorously as some silicone/perc/Al formulations I've made for groundworks (not intended for propellants, but...who knows?), but without the worrisome black smoke cloud he got when packed into a tube.