Best you hire a pet transport company - they will be the ones making sure your caiques get fed and watered. It'll be a couple thousand of dollars, but it'll be worth the peace of mind. Your birds will be travelling in cargo as Changi doesn't allow pets in cabin.
Here are two links you need:
https://www.nparks.gov.sg/avs/pets/...ranshipment-of-other-animals/ornamental-birds
https://www.sfa.gov.sg/docs/default...mport_doc803f461875296bf09fdaff00009b1e7c.pdf
Before you plan on leaving, make sure you can prove your birds originate from the US. The US typically requires 30 days of quarantine when you bring a bird in - if you prove they are American, then you can serve that quarantine in home, rather than a federal facility.
On the other hand, if your birds are healthy and clear government health inspection, they are unlikely to serve quarantine in Singapore.
Long story short, 30 hours is manageable. The big question is: can you return to the US with them? If you don't prove they are US-origin birds, then you have to ask yourself if they can tahan 30 days in a US federal quarantine facility.
On a side note, the government is tightening up on work passes, not just due to COVID but also due to tradition before elections

A lot of people are losing their work passes, including EP holders, and are unable to get new passes. Good luck!