It sounds as if that you HAVE NOT YET travelled the outbound from LAX. Which means that you are effectively cancelling the original ticket and re-issuing a new one.. which is correct at $150 change fee. (Or its $100 fee with $50 service charge to the consolidator).

Your best bet is to travel first to Chennai, and then from there to extend your stay in Singapore on the return. In Chennai, contact SQ who will then change your ticket.

Without knowing fully about your ticket, I cannot advise you. But SQ has so many different fares with different rules especially through consolidators. Travel weekday is different from weekend. Stopover outbound, inbound etc.