i4500 may not be 100% PSW, waveform is critical, your Magnum in order to work as a booster will have to have a 100% identical waveform in order for it to "add" support to the existing input from gen.
In order for your Magnum to be able to "sync" with and "add to" the incoming power it must be able to perfectly mimic the waveform and frequency it is seeing on the input. Failure to reproduce the waveform and frequency of the input will result in a fault.
The fact that shore power and the Magnum boost works fine with both ACs is very telling to me.
Do you have access to a non inverter 4Kw 120V gen to try a test?
Old school non inverter gens will have 100% PSW waveforms, the only caveat is the frequency will be a bit higher than 60 Hz (61-62 Hz) when unloaded and when fully loaded that can sag to 58-59 Hz.
Inverter gens while they may claim to have PSW output, in reality their waveforms can be badly distorted in spite of the marketing claims and that distortion most likely is causing your issue. I would put that Westinghouse brand in the questionable quality category for waveform.
Have access to a Oscilloscope? That would tell the tail right their, need a perfectly formed sinewave waveform (magnify the waveform on the scope to view the steps) , lots of little jagged steps means there are a lot of harmonics above 60 Hz which would indicate a series of squarewaves put together to create a close representation of a sinewave along with some output filtering to smooth out some of the harmonics.. Harmonics and jagged waveform can cause issues with how your Magnum will handle the load.
The fact that you can get it to work on shore power but fails with the i4500 tells me you are barking up the wrong tree, it isn't a fault or setting on the Magnum, it is something with your choice of gens..
Westinghouse (Which was known as Westinghouse Electric) as you may have grown up with does not exist, they do not make that gen, that name is "licensed" from Westinghouse brands licensing division.
Westinghouse nearly 20 yrs ago divested themselves and sold off all of the divisions until only the Nuclear division was the only thing they do and created Westinghouse Electric Company in 1999.. This new version of Westinghouse only deals with commercial nuclear power plants, they have nothing to do with consummer generators, TVs, blenders or any other non nuclear items.
Westinghouse Electric Company then was bought up by Toshiba (sound familiar?, yeah, semiconductor, computer memory and hard drive Toshiba) where they found out why nobody wanted the Nuclear division the hard way by bleeding them dry with losses.. Toshiba did manage to find another company dumber than they were to unload the Nuclear division at a huge loss to Toshiba..
That gen is simply a rebranded Chinese built gen with nothing to do with Westinghouse other than being officially licensed to have the name stuck on the side..
The current Westinghouse headquarters? Yeah, that is huge albatross campus on the edge of my county and hr away from me with a fraction of workforce the building once held..
Not sure what happened to the original Westinghouse corporate building in downtown Pittsburgh that I once worked at, I am sure it was sold and re purposed..