It's hard to predict social phenomena. I just try to react quickly when problems arise.
You could cap it right now, and see what happens to the quality of the site.
If limiting new accounts seems like the best solution, it should be done clearly and transparently - as the users you are trying to weed out are generally fickle and will not stay, so won't bother to check / sign up later. Let users know the reason why they can't sign up now, and when they should be able to.
However, users that have a legitimate need to comment (eg site / app owners) need to be allowed access - solving this could be trickier.
Not that this has any obvious parallels to HN.
Also, a lot of HN discussions are self-referential (esp. when discussing user testing, etc.). It would be really helpful to have some data to add to these discussions.
d(users)/dt is growth in users, not their number. To illustrate: if 600 users registered in February, then only 400 in March HN's growth would be negative; d(users)/dt would be negative.
d(users)/dt would be the rate of change of users. That can only be negative if the amount of users decreases, ie through bannings.
You're thinking of the second derivative, d^2(users)/dt^2, which is the rate of change of the rate of increase of users. If that is negative, it means that the growth has slowed down, as in your example with February and March.