[NY civil procedure] Correcting Minor Defect in Motion to Dismiss

Hi all, I'll flag I'm an attorney myself. Was not sure where best to post as LawyerTalk does not appear to allow this type of question.

I've filed a motion to dismiss for failure to state a claim under CPLR 3211(a)(7). However, I was unaware that strictly speaking, motion papers must include a copy of the underlying complaint. This had never been an issue for me before as my motion practice all involved e-filed cases, where the rules say that there is no need to attach the complaint (as the Court can simply pull it up on NYSCEF). But this is a physical case, and my erroneous assumption had been that the court would similarly already have a copy of the complaint in its record.

I would like correct this error prior to the motion return date, either through some type of supplemental affirmation/notice of errata which includes the complaint, or else as part of my reply affirmation to opposition, likewise including the complaint. I am also preparing to rely on CPLR 2001 as well as First and Second Department case law to argue that there's no prejudice to Plaintiff (as obviously they themselves made the complaint, i.e. I am not surprising them with new evidence or records) and that if the Court has a complete record at the time it's deciding the motion, the initial omission is therefore excusable. There is First and Second Department precedent where this sort of thing has happened.

Has anyone been in this position and can offer any suggestions or advice? Particularly the best type of filing to accomplish this supplementation of the record? Or let me know if there's another forum better suited to this sort of question? Thanks all in advance.