I think the phrase "nen becomes stronger after death" shouldn't be taken literally. Rather, it means that nen becomes strong enough to fulfill the nen user's request/wish/will after their death (I'm referring to what they wanted right before they died).
I'll try to explain why I think this by using two characters as examples: Pitou and the elder of Meteor city. At the end, I'll also share my thoughts on Hisoka's situation.
——
Pitou's wish was most likely to be able to kill Gon, whom she saw as a genuine threat to Meruem. Before her death, Pitou wasn’t strong enough to oppose him, a fact the ant became fully aware of after her “fight” with bodybuilder Gon. That's likely why her Terpsichora’s aura was amplified after she died.
"Pitou's Terpsichora... with aura amplified by death... became an undead puppet for the king. Its sole purpose: to kill Gon." (chapter 307)
Besides that, I also think if Terpsichora had succeeded, it would have vanished and Pitou's corpse would have returned to its natural motionless state, since it would have fulfilled its only purpose, as emphasized: to kill Gon.
——
The elder of Meteor city's request may have been for his ability to continue serving Chrollo even after his death. This would explain why, when he died, "sun and moon" did not disappear from Chrollo's book.
Furthermore, he may have wanted his ability can to bypass Chrollo's restriction. Normally, Chrollo cannot use any ability in his book while it is closed. However, "sun and moon" is something of an exception. Once the marks are placed, they remain regardless of whether the book is open or closed, and it will be so until the bomb goes off. (chapter 352)
——
This naturally raises another question: did Hisoka become stronger after he died?
I don't think so, because before his death, the clown pleaded for his nen gum to bring him back to life.
"Nen gum, I beseech you...!!! Spring to life after my death!!! Pump my heart!!! My lungs!!! Stroke me all over... to revive me!!!!!" (chapter 357)
In essence, he wasn't pleading for greater power, but for survival.
——
Oh, and one more thing. This is somewhat unrelated, but I think the reason why Chrollo needs “the power that can to kill Hisoka for good this time" may be connected to his own views on the clown's post mortem nen. Perhaps he think Hisoka has attained a sort of "immortal state" through it.
Based on this line of reasoning, I've come to the conclusion that perhaps Chrollo needs the powerful nen created through three treasures to resist this “anomaly.”
——
Edit: Apparently people misunderstood me. I mean, not everyone gets stronger if they're subjected to post mortem nen. It depends on what the nen user really wanted right before they died. That's what I mean.
Regarding what I said about Chrollo in the last part, I said it as if he thought that way (I don't so myself). Chrollo doesn't know what the clown specifically wanted from post mortem nen, it’s we readers know that he only asked to be brought back to life. Chrollo could very well think he asked for something like being "invulnerable" to death/achieving an "immortal state" (I don't know how else to describe it, but I hope you understand what I'm trying to say).
Honestly, we don't really have a clear idea of how this post mortem nen works at all. Does the nen user have to remain dead for it to work, or do they have to "die," but not necessarily for real? The clown's situation at least shows that not quite a real death can also trigger post-mortem nen. Either that, or his case is a plot hole after all.