Yes, "replication" in this experiments usualy means foloeing the oficial recipe and many small variants.

Publishing an exact reproduction is difficult, but a new record a few degrees hotter is easy. (And even another variant with a lower temperature and more tolerance for current or magnetic field can be published with the right text.)

I can't see why they'd skip replication given the uncertain status of the original process. They'd try to replicate as closely as possible, confirm they have a superconducting material, then they'd branch out from their established process. Starting from a variation means they don't know whether it doesn't work because of the variation or because it doesn't work at all.