Nice LCR Meter, the mentioned fixtures should plug directly into the 4 BNCs on the meter front panel, these are positioned such that the fixtures need no additional cables and have the right type BNC Connector
We don't have a 270uF 16V on hand, but do have a 220uF 25V which might be similar. Attached are plots showing a frequency sweep for 10Hz to 1MHz with our IM3536 LCR meter. Plots were created by python routines we developed as a means to do these type sweeps, as well a Voltage sweeps and even some temperature sweeps. Don't want to distract from your thread, but if interested will discuss and link.
Edit: Here's what the fixtures look like. Also added another plot showing how the effective capacitance steeply rises as you approach series resonance.
Anyway, hope this helps and you can see the series resonance around ~45KHz, which seems typical for these type electrolytic capacitors.
Best,