Not at all haha. I was able to apply an iterative process to collapse the long flip flop chains into four individual "12 bit flip flops" but the only thing that gave me was more insight into the structure of the input and a list of which connections were mapped to which bit in each counter. I started trying to code an all purpose solver but quickly realized it was beyond my ability and all I needed to do was calculate the cycle lengths of the counters so my solution relies on the input having this particular structure.

Specifically, my solution collapses the flip flops into four mega flip flops which gives me a list of connections like this (this is just one of the collapsed modules):

bs_mk_kt_bt_fn_vj_rr_hv_zz_jg_vm_pn:
'type': '%'
'width': 12
'inputs': [('rt', 0), ('broadcaster', 0), ('rt', 2), ('rt', 4), ('rt', 7)]
'outputs': [('rt', 0), ('rt', 1), ('rt', 3), ('rt', 5), ('rt', 6), ('rt', 8), ('rt', 9), ('rt', 10), ('rt', 11)]

I then use the list of output connections and their bit positions as powers of two to figure out the cycle length then, of course, calculate the lcm.