I haven't read through all the previous posts, so I'm really not up on this case. Did DHCR just issue a decision? If so, what is the date of the decision? Also, please send us a copy of the order.
Congrats for his losing the PAR. Look further up where I quite section 2529.12 of the RSC. That says that any part of the original order was stayed when the LL filed a PAR ... until the PAR is decided, so now nothing is frozen. If it were me, I would start withholding the retroactive part as specified in 2529.12 (unless you're going for a money judgement).
Having said that, nothing is over until it's over. So whatever you get, put it in a bank and keep it safe in escrow, just in case.
As for an Article 78, he would file that against DHCR, not you. You would have to discover if it's been filed and then become a party to the proceeding. In some cases LLs will not object, and neither will DHCR, but in other cases you will need to make a motion to the court seeking to become a party. The details as to how to do that are complicated (especially now with all the COVID craziness) and you probably should get some legal advice on A78s, or even get someone to do it for you, that is unless you have the ability to do it yourself. A few do, but not many.
In the short run you will need to contact DHCR's Legal Dept. Ask for the "attorney of the day" to see if they have been served with the LLs A78, and the name of the attorney to whom it has been assigned.
To be honest, unless you have some faith in DHCR (and I don't), and it depends on the size of the overcharge, I would not file an overcharge. Didn't they AD decision already say what you are owed? Can you take it off your rent going forward. Again, I don't know all the details of this case and making a general statement.
So first, I would get your monthly rents in order - reduce it to the amount DHCR specified. If the LL has not given you a lease, then there will be no increases as per a regular lease issue. I would not even pressure him for a lease. As long as he doesn't give you one, your rent is frozen.
Then I would figure out what you have overpaid since the effective date of the AD order. Did it specify treble damages or just interest? (BTW, that might be a reason to file an overcharge as DHCR should award treble or interest).
For any rent, you should send certified or by certificate of mailing. If they don't cash it, that's his problem. If you sent it, that is what matters. Does he enter the amounts and any payment into a monthly statement? or ledger?
And with any check or money order, ALWAYS write in the memo field what month it is for. LLs often try to take your current payment and claim it's for some month from years ago. It's called "earmarking" and courts often uphold this if you specify the month. You can also specify on the check "see attached letter dated July 18, 2020" or whatever. Then attach a letter explaining how much you're deducting from the current legal rent and why, pursuant to the AD order dated ___ and PAR dated ____. Just document everything.