Early on in Chapter 2 there's a description of Olivia's death that you guys didn't mention. It's in the second half of a lengthy sentence (you commented only on the first half):
"She subscribed to intellectual and scientific periodicals that would never otherwise have been seen in Cassionville, and when she read them gave them to the library, so that a stranger to the town - a drummer, say, just disembarking from a train and seeking an hour's innocent reading before a night spend at Abbott's hotel - would have thought the town to be a very hotbed of intellectuality when the fact was that you might have killed it all, if you were so fortunate as to possess a motorcar, on any spring day when it proceeded, with pansies and lily of the valley on its small hat, from Macafee's Department Store diagonally across Main Street to Dubarry's bakery."
Weer obfuscates the description of the death in two ways. First, he's stating it as a hypothetical, when it's so specific that it clearly must have happened. Second, he switches pronouns - rather saying "she" proceeded with "her" small hat, Weer says "it" proceeded with "its" small hat. In that clause, "it" refers to the "hotbed of intellectuality" which consists only of Olivia. (This is an inversion of the trick pulled in chapter one when a painting is referred to as "he/him"). I think Weer is speaking about Olivia's death indirectly because, as he later states, even after all these years it's still difficult for him to process her death. Yet he remembers the minute details down to what flowers she had in her hat, which makes it all even more heartbreaking.
So, assuming that this passage describes how she died, whoever killed her possessed a motorcar. I've read in other discussions that it's Professor Peacock, but I can't find a reference to him owning a motorcar, just that he took a train into town. (Side note, the drummer from the train also seems so specific it can't be random.) It seems pretty plausible to me that the whole conversation about death and murder that Weer, Olivia and the professor have never actually happened, but Weer's mind invented as happening since he knows the professor murdered her.
Isn't it odd that Weer never mentions anyone being punished for Olivia's death? I wonder if the event was a hit-and-run, and the driver was never identified. It's more tantalizing to imagine that Weer knows but won't say, and to wonder why but, at least within the text, there's not much to go on. At the time of Olivia's death, Peacock did have a car, but so did lots of other people, including Macafee, Smart, and Weer himself. You could argue that each of them had motive.
It looks like the source of the theory that Peacock killed Olivia is an article by Damien Broderick in The New York Review of Science Fiction. I haven't read it but am looking for a copy. At least one person who HAS read it says that it's only speculation.
The reference to Peacock's car comes at the beginning of Olivia's date with Stewart Blaine, and the description of Blaine's British car - Weer mentions that Peacock owns a car, but doesn't take it into Cassionsville, maybe to cultivate an air of 'scholarly poverty'.
Regarding the 'drummer', I think Wolfe is using this in the old-fashioned sense of a travelling salesman (a job his father held for a while during his childhood). A musical drummer would be so oddly specific as to be significant, but a salesman would be a generic example of a transient visitor passing through town.