That switch doesn't need so low esr capacitors, they probably used those kzg because they were cheap, they're mass produced for motherboards so they probably got a good price buying them in volume.
I've done some searching about why low ESR capacitors are necessary. For example, https://electronics.stackexchange.com/questions/109385/when-should-i-use-a-low-esr-capacitor
says
The requirement for "low-ESR" capacitors normally arises in output filters of switching power supplies
That doesn't seem to be what the 1500 uF capacitors are doing, they are smoothing the power supply for the big chips I think.
You should be fine using panasonic FR series, or united chemi con KZE and even KY, it should be good enough for that switch.
You could also do a polymer capacitor mod , for example replace the 1000uF 16v with 1000uF or even 820uF 16v polymer capacitors and the 1500uF 6.3/10v ones with 1500uF or 1200uF polymer capacitors. It seems like the 16v capacitors are in parallel (for lower esr or maybe they couldn't fit a single taller capacitor) so lowering to 820uF shouldn't be a big deal.
I think I will replace them with the polymer capacitors if that's an option. Clearly I have a lot to learn about capacitors.
What I mean is that the circuit requires Low ESR capacitors, since it's a switching power supply, but it doesn't necessarily need a capacitor series considered in the "ultra low esr" sub-category of the "low esr" category of electrolytic capacitors.
If the KZG series has 10 mOhm ESR for that 1500uF 6.3v capacitor, you can use UCC KZE with let's say 12 mOhm or KY with 15 mOhm and it's not going to be the end of the world, there's quite a lot of margin designed in these circuits. Keep in mind also that those capacitors were going slowly bad over time, with their ESR values and peak current ripple capabilities changing and the switch still worked until eventually the capacitors just got bad enough to cause visible problems.
This KZG series was designed for VRM circuits, the DC-DC converters which take 12v from the computer power supply and produce 0.8v .. 1.3v for the processor at up to 100-120A of current (spread across multiple power phases and multiple capacitors) and these DC-DC converters operate at high frequencies, up to 300-500kHz
The power supplies in your switch are switching power supplies, but they're not at the same level, they're way more simple and run at much lower frequencies, typically 60kHz to 200 kHz, and they basically convert 9v..12v to the voltages those chips need, which would be 2.5v , 3.6v, something like that. Basically, the power needed for the ICs.
In your particular case, one of the power supplies in the switch uses a switching controller made by Richtek, it's that chip RT9214 which runs at 300kHz .. You can see the datasheet here:
http://www.richtek.com/assets/product_file/RT9214/DS9214-15.pdfYou can practically compare the schematic in the datasheet with how the parts are arranged to the right and bottom side of the chip, you have the inductor (the wire around the ferrite), the two mosfets and the two capacitors to the right of them installed in parallel to reduce ESR and have enough capacity (due to height)
The KZG series was not one of those in the 2002-2004 times where Nichicon screwed up their HM/HN/HZ capacitors and a lot of Dell computers failed. It's also not one of those made with incomplete electrolyte formulas that were stolen. For a long time, UCC made this series but the electrolyte inside I guess was unstable, they aimed for too low ESR, and A LOT of them went bad even on shelves, not installed in computers, never used. If you see a board that's before let's say 2016 and it has KZG series capacitors, you can suspect them.