Apart from your engineering work, the label on the blue battery pack from Varta in German is also interesting.
You can actually only find labels like this in English, so I think the Varta battery pack is from the 1980s or earlier.
It works but the recylcing time is longer than with the original Ni-Cad.
Yes, the converter and the battery are limiting factors. The converter is rated at 0.5A at 12V, which is more of an issue than the battery. The actual measured converter output current can go to 1A but not sustained. The required battery current based on calculation should be about 4 times as much. The flash can draw several amps with the Ni-Cads, so it's obviously under powered. With the converter setup, the flash full output recycle time is about 50 sec, but on auto mode, indoor, it's still quite usable once the flash is initially charged.There are two things you may want to check: the current discharge rating of the cell, and current rating of the DC/DC converter. Continuous discharge rates for 18650 cells can range anywhere from 0.5C to 15C (1A to 30A in your case), but the cheap-as-chips converters tend to have a rating below 1A, so that's probably your weak spot. If you can solve that issue, you also want to accommodate a peak draw way above these numbers for the first few ms, so you might want to consider a cell without a built-in protection circuit, and similarly a converter design without a current limiter: you'd be overdriving stuff for the first few milliseconds or so, not long enough for any localised heating.
The red battery is Sanyo, The label says "UR 18650FM M43A", printed, "MJ5M4CA 007605".
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