Unfortunately I have heard that the Singapore government is clamping down hard, on recruiting from outside of Singapore, due to the amount of Singaporean jobs lost. I know some companies that had quotas, last month only to find them lost today, so my belief is, the doors are more than half shut! And that companies will be forced to take Singaporean labour like it or not, many need the skills of retraining, although many Singaporeans refuse to do certain jobs too, so its a bad circle for many. But I wouldn't be too optimistic these days of securing anything in Singapore just now.
Also the entrepass criteria is tightened because of the loop holes, and since many of those that have been given the chance, haven't contributed to employing Singaporeans, why let them in...all said and done, a fair warning was in the local press, that Singaporeans would be put first. So expect it to get worse for foreign talent seeking to come to Singapore.