You said we use cash to repay mortgage instead of OA. How about instead, we use that cash to buy S&P500 and OA for a mortgage? Won't buying the index with cash incur lower exchange/fund fees?

My personal preference is to pay mortgage using CPF - I would keep cash more for flexibility.

Buying index with cash might not necessarily be cheaper- it really depends the platform that you choose to invest in. If you use a low cost discount brokerage like interactive brokers then you would be alright.