Actually I just noticed that I made a calculation error. I had the elite bonus multiplier on the base + cabin bonus, which is incorrect. The elite bonus is only on the base miles. I just fixed it and you'd only end up at 110k-112k LPs now, needing to find about 13k-15k another way (Other flights, AA credit card spend, AA Hotels (I'm assuming it's still out there, I found one after the change this year where you could still get about 16k LPs for $500 and not need to ever visit the hotel).

Reversing the itinerary does work, but it would then ticket through JL (assuming it even works in the OW tool, I haven't tested that). So I changed it slightly to cause it to get ticketed by CX, but you'd lose MIA. Just be sure you're timing your start and end within AA's Elite qualification year (March 1st to Feb 28th). BA is different and your qualification year is based on the month you earn your first Tier Points (which I'm assuming you already have done in the past so it's probably already set, you can see in your account, mine is May).

HND HKG CX
HKG SIN CX
SIN HKG CX
HKG DOH QR
DOH HEL QR
HEL LHR AY
LHR BCN BA
BCN DOH QR
DOH LAX QR
LAX JFK AA
JFK GIG AA
GIG EZE BA
EZE JFK AA
JFK SYD QF
SYD MEL QF
MEL NRT QF

One caveat in this, you'd hit Gold during that DOH-LAX flight, and I don't know how AA handles that 40% bonus. If it only counts from the next flight then you're at 110k LPs + the 2x BA flights mystery amount. But if AA pro-rates it exactly from 40k LPs then you'd have about 4,400 more LPs than I've accounted for, which might also kick Platinum in sooner than I've calculated so maybe a couple thousand more LPs than I've accounted for.

The biggest difference (high fees aside) between AA miles and Avios is that AA is zone based for redemption and Avios is distance based. Very short flights in business class are a good deal with Avios, but their long haul redemptions are atrocious these days. AA has some really attractive long haul rates, but some of the short haul wouldn't make sense in comparison. It's useful to have both on hand. I have AA as my primary but I always keep some Avios active for specific shorter redemptions. AA also weirdly doesn't have all OW inventory for redemption. I haven't found very many examples of this but there are a small handful that I've noticed on JL and CX where BA would have availability on those routes, I think they fixed one of them after I lodged a complaint to AAdvantage CS but it took a while and I couldn't use it when I needed it.

For you, domestic, if you go with AA once you get to PPro you'd have some chance at upgrades but I wouldn't expect many, you'd also get free Main Cabin Extra selection at booking and 3x free checked bags on AA metal, but only would have lounge access on long haul international. (they were allowing Admirals Club on Caribbean and Central America as well for a while but not sure if that's still in place). If you go with BA you won't get the upgrades or MCE seating, but you'd always have lounge access regardless of itinerary. Your baggage would also go by the OneWorld Emerald policy which is +1 on top of whatever the ticket allows (which is usually zero on domestic economy).

It sounds like you don't do a ton of domestic flying as it is, so I think the big decision comes down to how you will use your miles. In the end, after achieving PPro once, it's easier to maintain. I think you'd likely earn a lot more miles with AA but depends on which airlines you fly on going forward. AA's tier bonus applies to all OW flights. BA's tier bonus for Gold only applies fully for BA, IB, AA, JL and partially for AY (maybe more, I just didn't find them), though I suspect those will be changing for at least BA and IB soon and will just be a higher multiplier on the revenue, just like AA for it's own flights in AAdvantage.