How come when I tested for connectivity of the wrist strap by connecting one probe of a multi-meter to the big metal of the wrist strap (the area that touches my wrist) and the other probe to the banana plug of the wrist strap, there was no beep sound?
The "beep sound" is only a crude indicator of "continuity". Where "continuity" is likely defined as a MUCH MUCH lower resistance than anything that should be found in a proper ESD protection scheme.
It is not valid to use the "continuity beeper" when analyzing/measuring high-impedance circuits as yours should be. It would be an interesting experiment to get a high-value potentiometer (perhaps 100K?) and experiment to see how low the resistance has to be before your "continuity beeper" senses continuity. I would expect it to be 100x or perhaps 1000x lower than anything that would be safe in an ESD circuit.
It is a good thing that your continuity beeper does not sound. If it did, you would be in danger of electrocution because your circuit is much too low resistance.