How did you go at Cx and KA? Did you feel it went ok. Or did you bomb out big time. With 250 hours and a frozen ATPL you will have a better knowledge of aviation and understanding of the industry which would stand you on good ground when you reapply with KA OR CX. Have you thought about applying to the Government Air wing. Sure it's not jets but flying J41 turboprops around for a few years before reapplying to CX would be a great opportunity and give you some "real" skills.
Jetstar Asia do a cadet program which I found out about by looking on their website just now. Must have the right to work in Singapore, their is a link to the Singapore immigration page to see if you are able to.
Their is a lot of aviation in Asia, check out their websites on employment or careers and see what they state.
Sure it will be difficult to get a job with only 250hrs, but you won't get a job with zero hours. Yes it's a risk but if you REALLY want it you'd go for it. If you don't have the passion, the drive, and the dedication to get out their and try don't waste your time.
Good luck. Make an educated decision. The aviation industry is a tough nut to crack.