Is the preposition 'an' really necessary here? Could it not be dropped, since 'vorbei' whilst being part of the verb seems - to me - to contain prepositions enough here to say as much....? vielen danke
vorbeispazieren is not a verb (i.e., vorbei is apparently not one of the removable prefixes of spazieren). As for vorbeilaufen, it seems that that IS a word, but usually referring to running, not walking, with that prefix.