Lightweight High Current AC Output

It possible and not actually that hard to do if you know your electronics and know where to get the parts! Technically the transformer less stuff still has transformers but they are small high frequency type and not the typical iron core type.

Your output would be 15 KW and given a 240 volt single phase input and about 80% realistic efficiency you would need about 19Kw input or around 80 amps or so. Thats easily within the range of modern high powered inverter type power supply.

Many compact welders and almost all high powered plasma cutters use inverter type power systems and run much higher power than that with modern switching technology.

So what do you need 5 volts at 3000 amps for any way? Running vista on a your new computer and need to power a couple dozen 3.3 Ghz quad fours in order to get it to run smooth?

Depending on the duty cycle a spot welder transformer can easily do much higher amps than 3000. Just by changing the windings it would be possible to get 5 volts out of one at 3000 amps.