Budget airlines ply cheap non-stop routes between BKK and KUL to most of your Asian destinations. Those flights are usually in the $100 (short, say bKK-SGN) to $150 range, plus baggage fees. Prices may be much less if you book in advance
You can check for LCC deals very easily on Skyscanner. Highly recommended.
I'd use your miles on TPE/HKG legs as those can get expensive. Try and book a trip to BKK via TPE/HKG and get the stopover there. Then fly out of KUL, for instance.
Don't miss a trip to Bali - it's not far from Singapore and you'll enjoy it much more!