[qupote]...ran thru 1 Meg Ohm resistors in place of the battery ...[/quote]
That's the key difference. There's virtually no current in a Meg Ohm resistor. Once a couple of amps flow, either through a battery or a resistor less than 5 Ohms, then you will see other frequency vs. current and switching "bounce" effects happening. But they are invisible when only a milli-amp of current flows.
Hey these screen-captures may also come in handy because questions about the wave-form come up from time to time. Now that you've posted a few pix they make for a useful reference when explaining what happens when the output is rectified. EG: the root-mean-square of a sine wave is the peak divided by 1.41. But when it's not sinusoidal, like the rippling DC as you show, the RMS is is only a little bit less than the peak voltage. Your pictures illustrate that well.