Milk won't be affected by time difference.
if you pump at 3pm in Sg, and its 3pm is 5pm, then you pump at 5pm. For pumping just follow Sg timings.
if you cannot store, throw it away is better than not pumping cos it's demand and supply. Or drink it back into your body.
if can find a freezer to store, bring storage bags, then bring back to Sg...you will need to figure how how to keep bags frozen on flight back.
this is a good problem to have. well done!