I don't know why you think it is a bad idea to apply to KA at the same time as CX. If you don't mind who you fly for and don't want to apply to all three at the same time send in applications to CX and KA at the same time. Then if you don't get in go for SQ. CX and KA would not give it a second thought. It is a positive not a negative to go for both as they are the same company. You would not be asked to attend anything that clashed with the other because they are the same company. Or go for SQ then CX and KA. In my opinion if you are the right candidate none of the airlines would care if you went for all three as if you want to be a pilot it would be stupid not to apply to all of them if you were eligible.