First of all I'd advise you change the heading of your thread before the mods ask you to. IE to make it more relevant.
Secondly in my opinion you only regret the things you don't do in life. So I'd say go for the month- it's a great opportunity to test living and working in Singapore- could your patrner come too?
Third, don't stress about the rest until you have made a decision on whether or not this new job would be a good opportunity or not. IF you decide it is something you would like to go for, THEN crunch the numbers and see whether you can afford to retain a new house, even on an interest free mortgage AND rent in Singapore or what is the best way forward financially.
In my opinion if the job is attractive enough then the relocation package should be also more attractive than taking redundancy.