It's the ideal thing to do for sure, but I've not got the use of a scope at the moment.
That's a pity. You *really* need that data to avoid throwing more money away.
What I am concerned about is whether the diode drop becomes excessive at your required load current - I expect the average output voltage to be under 13V and that adding more capacitance to maintain a higher voltage will be ineffective due to the increased peak current in the diodes increasing their voltage drop.
The discharge rate of the bulk capacitor can be calculated so you don't have to actually measure the slope, but it would be worth setting up to measure the peak and trough of the ripple under load using a diode and a capacitor
(Peak reading voltmeter is easy. For the trough reverse the diode and use a 1Meg pullup to a higher voltage. Calibrate out the diode drop using known DC input voltages) Also measure the mean DC voltage, and ripple directly using the capacitor for DC blocking as a cross-check. You'll need to know whether the DMM is true RMS or half or full wave average (try both polarities!), calibrated as RMS equivalent for a sinewave, as you need to convert the ripple to a pk-pk voltage.
Another option would be to use an Arduino (or other MCU with ADC and UART) as a 'pooor man's' oscilloscope.