I would advance the theory that it's not the Blunami board unless the board is defective. As others have said, you have a board capable of delivering plenty of power to the load.
Your wimpy AC-DC converter is almost certainly the issue!
- It's an unregulated power source, so it's output voltage drops as the load increases. By the time you get anywhere close to 1 amp, the output voltage is probably down at least 30-40 percent!
- The supply has a small 470uf capacitor, not nearly enough to deliver even one amp without significant ripple. I'm guessing by the time you are supplying an amp, the ripple is many volts!
You need to consider a switching power module with at least 2-3 amps max output!
Consider one of these. It has more power output, and it's a constant voltage output. I think you'll find that it works much better than that lame power supply you have.