I think an option for you might be a SIM-only plan. Normal postpaid plans in Singapore are unnecessarily expensive, because they need to finance your free phone upgrade every year or so. Unfortunately, there's not that many options for plans without phone. Here's what I found:
- Starhub has a new SIM-only 4G plan which apparently starts at S$13.95 a month.
- Singtel has a configurable SIM-only plan, which starts at $S20, maybe that's the one you already have.
I haven't actually used any of those, so I'm not entirely sure whether there are any hidden costs.
If you are considering prepaid, all the providers allow you to top up online with a credit card, so you shouldn't have to worry about that. However, they have this funny thing where your credit comes with a validity date. For instance if you buy a S$10 M1 top-up, it will be valid for 120 days, (See on this page under FAQ) which would be significantly cheaper than the cheapest price plan with the downside that you'd have to remember to buy credit every 3 months.