I called AA looking for a BKK-SEA-JFK-BKK award in J, believing that I was entitled to one stopover in the country of destination. They said SEA is not a valid stopover between BKK and JFK, so I would have to get two awards, one for BKK-SEA-BKK and one for the domestic sector (SEA-JFK). So they've booked BKK(JL)-NRT(JL)-LAX(AS)-SEA//JFK(AA)-NRT(JL)-BKK for 110,000 miles and SEA-JFK for 45,000 miles.

I wanted to confirm their interpretation of the rules- must my stopover in the country of destination be at the international gateway (as they say), or do I have flexibility in stopping at any point on the way to NY?

Oneworld awards shouldn't matter on cities used, though that might depend on your program
If not, then SEA is your destination, and JFK would be a stopover at an international gateway

When I tried it as a BKK-SEA-BKK award with a stopover in NY, she said that NY would not be the international gateway, but it would be DFW or LAX.

I may try and call back and get another agent. I just dropped from EXP to PLT and this was my first experience with the PLT Desk (if there is one). Not impressed with the agent's knowledge of the rules.

That tickle in my brain is that you and/or the AAgent are looking at AA and not OW awards. If AA, then they would want you to touch down in one or another AA gateway city in the US. SEA is an AA gateway from... Texas (which I am increasingly believing is a strange foreign land anyway.) Thus somewhere on the west coast like LAX, or some other AA longhaul gateway ex-Asia, such as DFW or ORD. Maybe my knowledge of the rules is seriously lacking here, but regardless, a workaround came to me.

According to the old Great Circle Mapper (YMMV - but I hope not by much) the following routing (or its reverse) could qualify as a OW Distance Zone 6 (14,000 - 20,000 mi) trip, 130K mi in J - BKK-LHR (BA or QF)-JFK(AA)-YVR(CX)-HKG(CX)-BKK(CX) coming in at 19,279 mi; if you wanted to forego NCW you could go BKK-HEL(AY) -JFK-YVR-HKG-BKK for a couple hundred miles less. If you're in love with AA 757s, you could go BKK-LHR-JFK-SEA(AA)-YVR-HKG-BKK and still stay under the 20K limit. If you can't use the AA codeshare (Horizon/Alaska Air metal) from YVR to/from SEA, take the train for 30 bucks.

By going east as a round trip instead of west, you're caught in the "AA plus 2" catch (i.e., if you use AA at all you must use 2 other OW carriers) unless you go BKK-SIN on AY, then SIN-HKG-YVR-JFK-HKG-BKK using CX for all other segments. Alas, any permutation via SIN comes in over 20K miles, hence bumping you to a 150K mi OW award (which is still less than the "use two" rule quoted by the agent.)

But by going RTW instead of there-and-back, you can stay under 20K miles and have lots of hours in CX, BA and/or QF J instead of AA.

Actually I have my own question about oneworld awards and transits.
Can you transit your departure city?

Eg. could I do this?

LHR-MAD-DKR (stop)
DKR-MAD (stop)
MAD-LHR-BAK (stop)
EVN-LHR

Or would I have to do something like:
MAN-MAD ... etc

Gardyloo, we need to go to SEA followed by JFK. The tightest route I found, bkk-nrt-lax-sea-jfk-hkg-bkk comes in just over 20k.

If using a oneworld award, AA does not count transit cities, only the stopover points. So only the mileage BKK-SEA-JFK-BKK should count, this would let you do an actual route of:
BKK-HKG-YVR (CX)
YVR-JFK (CX)
JFK-LHR/HEL-BKK (BA or AY)

You wouldn't be able to do LAX-SEA on a Oneworld award, as this is an Alaska codeshare. You would have to route this as HKG-LAX-DFW/ORD-SEA

Right - my suggestion was reversible - BKK-HKG (CX)-YVR (CX) then surface to SEA (3 hrs by car or train; 40 min by cheap air shuttle) then YVR-JFK (CX) or SEA-JFK (AA but it's a 757)-LHR (AA) or JFK-HEL (AY) then LHR-BKK (BA or QF) or HEL-BKK (AY). On OW awards you don't have to return by the same route, in this case you're doing essentially a quick RTW. As long as you use 2 OW carriers (if no AA in the mix) or AA plus 2 other OW carriers if AA is used, the OW mileage-based awards have more flexibility than the AA awards alone. Your AA miles can be used either for the OW or AA awards - look at the AAdvantage website.

Nope, you cannot transit/stopover your departure city. You would have to do as you suggest: MAN-MAD ... etc.

Also, AY flies BKK-HKG (only certain days however), so you could get a OW award on AY/CX

BKK-HKG-YVR (AY/CX)
YVR-JFK (CX)
JFK-HKG-BKK (CX)

Though really, it's about the same distance to go JFK-BKK via London or HKG

AAPLT Desk cannot get any availability on CX on those dates. They are suggesting I take the two awards and go BKK-NRT-LAX-SEA-JFK-NRT-BKK. My other alternative now is UA on a paid ticket- $3,200 for BKK-NRT-SEA-LGA//JFK-NRT-BKK. I'll try to see if CX opens up over the next few days, otherwise I'd prefer to pay for a UA ticket rather than shell out 155,000 miles.

Aside from the question of availability on the dates that you want to travel, some agents are not familiar with transit rule of less than 24 hours, especially on OW awards. Perhaps, you could travel BKK-HKG, overnight in HKG, then try for HKG-YVR the next calendar day. I have award availability to be very good on CX, except for the usual odd days when everyone wants to travel (not necessarily peak times from a US perspective).