. . . I cannot convince myself that the latter part of the sentence is grammatically correct.
"No, something else in him had died, something that he had long desired should perish."
Hello, MileSim, and welcome to the Grammar Exchange.
I have enjoyed reading your dialogue with Gustavo in this thread very much, and I share your sentiments about his awesome abilities.
I thought you might enjoy seeing a syntax tree of the noun phrase (NP) "something that he desired should perish." I realize that some of the labels of the phrase nodes may be foreign to you, though you probably recognize VP (verb phrase). The relative clause is the upper CP (complementizer phrase).
The TP (tense phrase) nodes used to be called S (sentence) nodes before advances in generative grammar which made the new designation more desirable. There are, as you can see, two TPs ("sentences") within the noun phrase "something that he had long desired should perish."
The relative pronoun "which" is the subject of the lower TP, within the "that"-clause complement CP of "desired." As Gustavo points out, the "that" needs to be deleted or silenced in syntactic circumstances such as are found in the example we are considering.
In generative grammar, the relative pronoun of a relative clause "originates," in deep structure, in the position where its grammatical function within the clause lies, and here that is as the subject of "should perish." The relative pronoun "moves"/"raises" to the Specifier position of the relative clause CP.
I realize that the presence of both "which" and "that" at the top of the relative clause may seem strange to you guys. In modern generative grammar, "that" is not considered to be a relative pronoun; so when it functions as if it were one, that means that there is a silenced "which" or "who(m)" in play.