The higher voltage does mean that current will flow, regardless of some resistance. And consider that power does the damage, and 0.03 amps x 3000 volts = 90 watts.

Chinese manufacturers tend to overstate their product performance, thus this unit may not reach any of its stated maximums. But if "two out of three" are actually achieved, one of these should be true (unless my calculations are wrong):

Maximum voltage and amperage (your calculations):
3000 volts @ 0.03 amps = 90 watts

Maximum watts and voltage:
25 watts = 3000 volts @ 0.00833 amps

Maximum watts and amperage
25 watts = 0.03 amps @ 833 volts

I suspect that either the second or third option is closest to reality. Nevertheless, if I build this theoretical fence charger and it is overpowered, I can always reduce its output with a resistor, correct?

 

The system in post #20 will certainly be effective. But one caution. I had, for a while, a nean sign power device that was not a normal transformer. I was some sort of mains powered inverter high voltage device that did not supply voltage "instantly" like a transformer does. If you get one of those it may not reach full voltage during the on time. So you may need to adjust the on time a bit. But you need to assure that the off time does not allow time for a predator to cross the wire "uncharged."

 

MisterBill2, thanks for the heads-up about the possible delay in supply voltage from an inverter-type power supply. I have an inverter-type portable stick welder that's ridiculously small and lightweight when compared with traditional transformer welders, and this makes me wonder if this very small and lightweight NST might also be an inverter rather than a normal transformer.

I decided to investigate this NST more thoroughly online, and it seems that it may not be suited for use as a fence charger power supply because someone on Amazon claimed that "these transformers will fail prematurely if allowed to arc".

 

Certainly there are now inverters made for lighting signs. One easy way to gain a hint is to weigh your device and compare that weight with a transformer of similar wattage. Another simple check is to balance it to see if the center of mass is close to the physical center. A transformer would be close to evenly distributed weight, end to end. If all the weight is toward one end then it is probably not a plain transformer.
If it is indeed a fragile inverter than you can still use it, just being very careful to support the wire so it will not arc to the fence. Stiffer wire and supports more closely spaced will be the way to go. And you might consider having it constantly energized instead of pulsing it.