Just a note of caution about AC voltages.... an AC voltage refers to the "root mean square", or
RMS voltage. The peak voltage of an AC waveform is commonly about 40% higher than the measured RMS voltage, so you are giving your LEDs a tiny little blast of 10V sixty times each second.
Your voltage readings are correct. With the resistor in place the circuit should draw approximately 65mA. That should not be enough to sufficiently drop the voltage coming from the power supply, so you should not expect to see a difference in voltage whether you use the 100 ohm resistor or an open circuit (infinite resistance, no current.)
To prolong the life of your LED's you need to drop the current flowing through them. I would try using a 200 ohm resistor in series with each LED. Alternatively, finding a lower voltage power supply should do the trick, too.
In the meanwhile, take some satisfaction in knowing that you have been successful in creating the very advanced device known to my students as the DED, or "Darkness Emitting Diode".
Jason