These days almost every consumer wall wart style power supply is a switch mode affair, so the 'secondary' ratings don't correspond directly to the characteristics of the transformer. The specified secondary voltage will be the actual output voltage. 31-34V would correspond to about ten LEDs in series, so that's probably how the string is set up. If at any point some of the LEDs are off while others are on, then half of those series strings of LEDs will be arranged antiparallel to the other half, and the output of the adapter will be a full bridge. The adapter will switch the output polarity to select which set of strings are on, or rapidly swap polarities to illuminate both at once (well, alternately, but persistence of vision completes the illusion of simultaneous illumination).
The two different output voltage ratings are a little funny but may be an artifact of there being some sort of current limiting internal to the adapter. You could measure the open circuit voltage and the loaded voltage to get a better sense of what's going on. Just be aware that if it does the antiparallel thing then you'll probably need to measure with an oscilloscope rather than a meter.
The built in current limiting may be (or probably is?) just a fixed resistor, but it's possible it's more sophisticated, or current limiting is built into the converter itself.
An additional resistor inserted in the string is probably the easiest way to go, although you'll need to find the right place to do that so that it ends up in series with all of the LEDs. A spot near the plug where there are only two wires in the string would be a good place to start. It's possible that if the adapter has some sort of active current limiting that it will act up with additional resistance, but I doubt that's the case.
You'll of course need to ensure the resistor is rated appropriately for the power you'll be dissipating, but if the whole adapter is only rated for 3.6W that shouldn't be too hard, maybe 1/2W at most?