Nice garden path sentence title there: both "jams" and "bat" have several completely different meanings and it took a while until my brain permutated the right ones.
(Tiger moth) jams (bat sonar).
(Tiger moth) jams (bat sonar).
Both 'tiger moth' and 'bat sonar' are noun phrases in which the first word is not the actual meaning of the phrase. So you have two of these weird noun phrases, topped off by ambiguity about the verb ('jam' vs 'bat').
Very tricky sentence to wrap your head around!
That's not weird; it is the norm for English by a ridiculous margin. We do have some left-headed compounds ("pickpocket"), but they are very noticeable exceptions to an extremely strong rule.
No, the normal thing to do in modern English is to say "pocket picker"†, where the head of the phrase comes after the modifier. As you note, the other order remains possible in non-archaic forms ("tryhard", "kiss-ass"), but it is unusual.
"Roast potato" is already right-headed; it is a kind of potato, not a kind of roasting or an entity characterized by its practice of roasting.
† That is, the normal way to express this kind of concept, not the normal way to express the particular concept of a pickpocket, where a conventional word already exists.
'pocket picker' illustrates my point though, you swapped the verb for noun form, and it became the other way around.
'kiss-ass' is the same again, or at least it arguably is. (And I would argue it: it alleges a person to be one who 'kisses ass', not who is the kiss on the ass itself.)
No, "pickpocket" is already a noun, and it means "pocket picker". Just like "kiss-ass".
'kiss' ...
There is also an extremely marked, almost-never-used way to do it, and "pickpocket" is an example of that.
What are you trying to say?
Also, while they're not weird for a native speaker, a lot of other languages would also mark the adjunct or head noun somehow to remove any ambiguity.