You don’t say where in Asia you are going, but look for options that have plenty of veg and protein – stir fries would be great, or veggie curries perhaps. Things to avoid are all the things you are already avoiding – rice, noodles, pasta, root veggies and anything flour based. If necessary, think outside the box – for instance you could have a burger, but not the bun or fries. Providing you stick to the principles of the BSD and try to keep portion sizes sensible, you shouldn’t have any problems.
Have a great trip.