Overlaps a lot of Usermark's suggestions, but a bit different.

TPA-MIA-LAX: The Miami to LAX is on the 763, which is basically (imo) AA's second best plane. I haven't taken it since they restarted using the 763, but I took it before and the service was good.

LAX-LHR: May the suite gods be with you.

LHR-DXB-LHR: Only way of getting to Dubai and back.

LHR-HKG-SYD: Enjoy Cathay First.

SYD-DRW-CNS-BNE-AKL: Your intra-SWP flights.

AKL-MEL: You would need to buy this on your own. I am going to go out on a limb here and assume that service and luxury is more impt than price. Emirates runs the A345 on this route for abotu $600 in First. That's with the suites with the doors and all. With this ticket, you also get car service in Auckland and Melbourne if you stop.

MEL-HKG-SIN: Again, enjoy CX first.

SIN-HKG: I would add another flight in here, not as a turnaround but with a few days stop. Bali, India, Malaysia, Tokyo, etc. Best experience will be on the nonstop Tokyo flights.

HKG-PVG-HKG: This one you're on your own with.

HKG-JFK: The nonstop can be hard to get from reports on this board.

JFK-MIA: I don't know if the flights fit, but AA does run a 762 on this route.

MIA-MCO: You will need to go into MCO instead of TPA because if you go into TPA then your trip ends.

MCO-XXX-TPA: Fill in the XXX with a flight that services both MCO and TPA. LGA, ORD, SJU, DFW, whatever. You just can't leave the country.

So the Oneworld part of the trip would be:
TPA-MIA-LAX-LHR-DXB-LHR-HKG-SYD-DRW-CNS-BNE-AKL//
MEL-HKG-SIN-HKG-XXX-HKG-JFK-MIA-MCO-XXX-TPA

BUT....

You have put a constraint on your trip that I would rethink. That is, you are squeezing a lot into a short amount of time. Flying does take time, so you're really looking at very short stays in each of these cities.

Here's what I mean. You leave Tampa (a lovely city, I might add) on the 12th. You leave through LAX, arrive in London on the 13th, and arrive in Dubai the morning of the 14th. You say a night and leave on the morning of the 16th (1am). You arrive in London later that day. You leave for Hong Kong that evening, arriving on the 17th, and then leave for Sydney, arriving on the 18th. You stay a couple of nights and go to Darwin. Stay a night and leave for Cairns. Stay a night and connect through Brisbane to Auckland. It's now the 21st. Here, you can stay two nights. Head to Melbourne on the 24th, connecting via Hong Kong to Singapore. Arrive either the 25th or the morning of the 26th.

So, you have stayed one night in Dubai, two in Sydney, one in each of Darwin and Cairns, and two in Auckland. I am tired even thinking of it. That is a hell of a lot of traveling for those short of times. Doesn't matter if you're in first or not. And add an Asian side trip, that just takes a couple days more.

What I would personally do is to go the other direction, time permitting. I would go to Australia first:

TPA-MIA-JFK-HKG-SYD-DRW-CNS-BNE-AKL//
MEL-HKG-SIN-HKG-LHR-DXB-LHR-LAX-MIA-MCO-XXX-TPA

You'll have more time in Australia and NZ and things will be less rushed. This, of course, assumes time isn't completely constrained.

With this routing, you leave on the 12th, connect via Hong Kong and arrive in Sydney on the 14th. Stay three nights in Sydney, two in each of Darwin and Cairns, and three in Auckland. This makes it the 24th. Go to Singapore via Melbourne and Hong Kong, and arrive the 25th or 26th.

So instead of six nights in the SWP, you have 10. Stop in Dubai on the return for a couple of nights, and head on home.