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PowerJack in the past has made some "3000 Watt" Step Up / Step Down Transformers.
Like with most things PJ, that rating is hard to come by. If stepping up from 120VAC to 240VAC thru the supposed input for the 120, you find that the socket, and receptacle on the cord, are rated at 10 Amps/125 or 240 Volts. Simple math there tell you that you get 1250 Watts max. Now as the units also allow input thru the same type socket on the 240VAC side, there again you get limited to 2400 Watts. Now if you feed it thru the terminal strip, you could input 30 Amps on 120Volt Line 1 and Neutral and expect to get 3600 Watts across L1 and L2 if the toroidal transformer were wound in a normal manner where Line 1 on the input would not also be Line 1 on the output. But again, we are dealing in Chinese Watts here. So that means that the transformer is wound as an auto-transformer. Now what does that do for it? As Line 1 is a common and Neutral is the center tap, Line 2 is derived off of the transformer magnetic currents. You can't use the 30 Amps 120 for input because................................................................................... when you look at the label on the transformer, it is only rated at 1350 Watts. So no Chinese magic here where 1350 Watts 120V in and 3000 Watts 240VAC out. Only if you feed 3000 Watts 240 VAC in can you get 3000 Watts 120VAC out. By using both legs and the center tap as a split phase unit. It does have one advantage though. If you feed it 400Hz, it still works. In fact it works over the whole range of 0-400 Hz in my testing. With no humming.
I had almost forgotten about it till you posted about it. I got one of those a few years ago cheap in an ebay auction. Didn't really have a use for it, so never even took it out of the box. Just now looked at it to see if it was the 3000w model you were describing. Yep.
The return address on the box is from Sean G. in Lansing, Michigan! Small world.
Despite not making its claimed rating (big surprise there!), it sounds from your desciption like it would work ok at lesser wattages.