I doubt AA staff at Narita would know about comping. They might know it. I talked to an AA agent in TYO last year and I asked her to check with the sales department. She called me back a few days later and asked all kinds of questions such as how much I make a year and what profession I am in, etc. She said she needed such info for submitting a request for comping.
As for BKK-NRT-DFW-DEN, if you are flying business, I guess you would qualifty for Plat. challenge.
If economy, then I think it's enough for gold challenge, provided that you take JL's codeshares as AA flights and they count as AA miles.
You have to choose either Plat or Gold challenge before you start it, I think.
If you also fly CX economy and don't live in Canada, it will not be counted toward mileage. I don't exactly remember but I think ex-BKK, AA uses M or S for the CX sectors.
You wouldn't bother flying UA or TG or the like, I suppose.