Issues like phase non-linearity cannot be fixed with an EQ- it usually makes it worse! Measuring and using a parametric to compensate can help response within the room but it cannot fix room problems which are usually at the heart of most of poor performance issues.
Bad idea. You won’t get there, and inserting another piece of equipment in the signal chain is also not optimal. Save up for the real thing rather than throwing $$$ down the drain on an equalizer. My $0.02 FWIW.