Asteroides has done an admirable job of answering the precise question as posed. This self-answer is just a follow-up based on the Olsen monograph to give a bit of the broader picture that I had not realized when I formulated my question, and to give a less technical presentation with some concrete examples in Greek.
In Greek, this family of PIE suffixes leads not just to τρον and θρον but also to τλον, θλον, θρη, and θλη. In Latin, it produces all kinds of things like trum, brum, bra, crum, culum, and clum.
The rules that Olsen proposes are I think, in dumbed-down form:
(1) If the root ends in s, then the ending has tr.
ἄγκιστρον, fish hook
This rule is absolute, and to me as an English speaker it seems to be closely related to ease of articulation. I find it very hard to say the consonant cluster στλ, and to a lesser extent σθρ and σθλ.
(2) Else, if the root has a liquid, then the ending has tr or θρ.
(3) Or if neither 1 or 2 applies, then we get tl or θλ.
χύτλον, libation, that which is poured
γενέθλη, race, birthplace
There are many counterexamples to 3 in Greek:
She explains this by saying that Greek developed a later preference for τρον, and that the vocabulary involved is often technical terminology, "later forms," or "foreign elements."