I base this on what slots the word can fill in sentence templates: e.g., the following is not grammatical for me: "my toes are very popsicle".

That's indeed an adaquate way to sort it out. It does not play much in our language, because we tend to glue the "compounds" together, f.i. witness stand is 'getuigenbank', numerical strenght is 'getalsterkte'. Pure nouns.
So it is more confusing in English but your 'mnemonic device' is very helpful.