jarchie, sorry, been quite busy, so I haven't finished with experimentation.
There's no need to apologize! I was just curious.
My current plan is to first try it attached to three AA batteries, to see that I do get a decent output when there's no ripple.
That sounds like a smart approach.
Assuming that works, I then plan to try and ensure super-clean power right next to the module.
If the problem is power ripple, I suspect the Ice Tube Clock power supply circuit is not able to sufficiently filter noise from the AC adapter. I suspect that noise filtering, as you suggest, is the most logical solution.
I'm not sure how much ripple is due to the power usage from the various ATMEGA chip subsystems, but shutting down USART, SPI, and the timers might be worth trying. I cannot write the code off the top of my head but can figure it out pretty quickly by looking at the ATMEGA168V datasheet, if you're interested. And if you are interested, please let me know which firmware you are using. Many of the alternative firmware projects have their own quirks...
I'll update this thread when I've got some kind of result. Thanks for your help so far!
You're welcome, and thank you for the update. I will look forward to learning how the project turns out.