you should hand clean it back to new, it will not remove the filtration bac, the important part. making the tank itself kill and digest the mass internally of all that waste is only one option, it used to be the only permitted way. we stopped doing things that purposefully make a tank look bad in some cases, you're free to. cleaning cannot undo the progress of any cycle at all.
if awaiting X weeks for it to self correct and make room for new corals after the cycling date is how you want to proceed, you can experiment with the common options and dosers and animals. imagine the freedom though in reefing where even if the tank is 5 years old and staghorned with coral, you can just lift out a rock, set it on the tank edge and knife off a chunk of algae that will never have the chance to take over. rarely, cuc usually keeps things in check. you provide final say before takeover with noncompliant zones.
the rest of the world would let it invade the entire system, then dose fluconazole. choose your order of ops, you cannot harm filter progress at any stage of cleaning or water changing. there is no boost nor benefit to the system in letting it self invade and then hopefully come back, that practice comes solely from the dated belief that water changes can undo a cycle (water changes=cleaning)