[old_tv_nut]

The jail bars frequency is in the 100 kHz or so range. It takes significant inductance to resonate at that frequency with the caps that are across the diodes. Take your spare cap and connect it across an existing diode cap and see if there is any difference. You don't have to remove the existing cap to see if the capacitor across the diode is having any effect on the jailbars. If you do see an effect, you have a starting point for investigating from there. If you don't see any effect on the jailbars, you can stop wasting your time and look for some other cause.

This advice is based on the caps in question being across the diodes as you describe and not from one end of the diode to somewhere else.