hate to rain on your parade, but theyll prob not extend ur exit
permit. Theyre pretty unreasonable in that respect, they want you
to be in singapore before you turn 21 and able to renounce
singaporean citizenship. And best part, is that they'll make you
wait 6-8 months before enlisting, unless you have connections, then
u can take ur medical in advance and go back to the US to wait out
those months.