I think, most likely, when you select the 80m band on the amplifier that it's band pass filter is designed to suppress all RF higher than 4mhz.
Band pass filters are not perfect, and that is why you get some power output between 4 and 5 mhz.
I think you are asking the amplifier to do something it is explicitly designed to prevent.
For comparison, my SGC 500 watt amplifier is set to band 3,which according to the owners manual supports 4.2 to 7.7 mhz. It is rare for me to use Mars frequencies outside of this range so I leave the band pass filter on band number 3 almost all of the time.
My amplifier is designed for use on all HF frequencies, but I think your amplifier is designed for use only on the amateur bands.
Regards