Unfortunately I don't know enough about sound equipment and the specifications
. I have a background in electronics and some audio knowledge but I'm not familiar with what is available.
With cheap equipment I imagine you will get a lot of "hiss" when you try to amplify the higher frequencies without some sort of noise reduction which might mean a DSP-based solution.
You could try attenuating the base and turning the volume up but depending on how the sound processor or equaliser works that might produce different results to turning the volume down and amplifying the higher frequencies.
If I were in the situation I'd look at either a small form factor PC or laptop with the correct audio IO and use a sound processor in realtime. Not sure if that will introduce noticeable delay or not though. I'm guessing ii will add some, as would any DSP solution.
Maybe you could try it on a PC first with some audio processing software just to see if that is viable using a movie file or something. I know a stand-alone unit would be better but I can't suggest anything specific.
@Mick knows about audio stuff but not sure if about equalisers for this purpose.
Is there any way you could try it with your existing equipment but using a different audio output to some sort of equaliser (you might know someone with one in a garage or somewhere!) just to try it?
Are there any specialist audio shops where you are that could advise or let you try etc?