Filtering power for attiny2313
It's almost certainly a lack of ground along the signal path. The power conditioning looks great.
Try cutting some track and wiring up a ground to run on every signal cable. This will reduce inductive coupling a bit, and is just good practice. You have the spare wires.
You could also make an aluminium foil shield for the whole case, connected to signal ground and mains earth. (5 sides of the case would be enough).
But the simplest fix is in software. As the LEDs are &quot;only&quot; for humans to see, they don't need to update very fast. Add some glitch tolerance to the ATTINY firmware, that it only changes output state if the input has been present for 20 ms or so.
Longer for the siren.
I usually do this with an 8 bit counter - read the pin 10000 x per second. Increment if it's high, decrement if it's low, but do not wrap. Then consider values &lt; 127 to be 0 and &gt;=127 to be high. That way a short transient won't change the display state.