So according to the calculator, LATAM flights get Asia Miles but no status points and Qantas flights get Asia Miles and status points. Does anyone know what happens if its a flight operated by Qantas but marketed by LATAM? I assume it would be treated as just a LATAM flight and get Asia Miles but no status points?

Based on the Asiamiles partner website, LA-marketed flights must be operated by LA, an LA affiliate, or CX to earn Asiamiles. In your situation, since the flight is operated by QF, it won't earn anything at all based on the rules. However, since both the marketing and operating carriers are CX partners, you might get lucky by just submitting a boarding pass for a retro-claim (but that could be a goodwill/exception)

BTW I suspect you are talking about the LA806/807 SYD codeshare. These are very special codeshare flights (evidenced by their 3-digit flight number) and LA gets a fixed portion, roughly half of the plane, to sell. You can see on its seat map that the LA flight only sees rows 4-7, 42-43, and 48-54. Before the pandemic, it was even noted LA would publish award seats on these flights (whereas usually only operating carriers release award seats). That is to say, it is entirely possible that CX just treats this flight as a normal LATAM flight.

If this is too much uncertainly, perhaps a stopover in AKL or MEL isn't too bad as well

It is indeed. Alaska specifically carves these out from eligible flights for earn. I would just rather do the QF flight given the Chilean part of LATAM is still running 2-2-2 business. I also called CX to see if I can just book it as part of a SCL-SYD-HKG ticket. The guy said he can find the flight on QF code but can't price it.
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According to ExpertFlyer, the CX fares to/from SCL require a CX flight to AKL/LAX/MEL/NYC/SYD/MAD/FRA, and then a CX/LA/LP coded flight to SCL. For MAD only, the last flight could also be IB coded.

And it looks like CX only codeshare with the LA flight on MEL/SYD to SCL... so it is right that the agent can't price the flight in QF code.

Is QF staggered J really that much better to forego the Club Points and AM if booked all on CX? Having flown both I personally found the LA 2-2-2 to be more spacious and a more comfortable bed to sleep on for overnight flights (although the lack of aisle access for the window seat is bummer)

To each their own of course but to me, yes. I have flown the LATAM 2-2-2 a while back as well. The point of business to me is the privacy. I don't want to be sat next to a random for 18 hours (including the 2 hour layover in AKL). There isn't even any middle 2 left. I would maybe consider that but the wing 2 are a no go for me. I don't want to wake someone up or be woken up in the middle of night if someone needs to use the men's.

I could try booking the LA code on the QF operated flight but I doubt I would get anything even in that case. Also, LATAM doesn't get status points, only asiamiles.

This is also vague on the CX Status Point calculator, but you should earn club points for any CX-marketed flights, even for ones operated by non-OW partners (CX*LA would earn club points as if it's a CX flight). If you make a dummy booking on the CX website, you can see that you earn club points for both segments. However, if you booked the LA code, you would only get Asiamiles.

Fair on the privacy point. Guess the use case is a bit different between an 8-hour overnight JFK/MIA-SCL where most go straight to sleep, vs 18 hours people inevitably need to get up

LATAM fly SCL-MEL non stop, so without the AKL transit
QF fly SCL-SYD non stop QF28 (LA807)
LATAM fly SCL-AKL-SYD.