Your budget is tight (to match the quality of the IDA-16). Can you build speakers yourself or assemble a kit and finish the outside of the cabinet?
Additional questions (so we can have a good idea of what kind of sound you are after):
What was your previous amp and why did you replace it? (Just trying to get a feel of the changes your system is going through.)
I note that your stated budget is less than the retail cost of your current Def Tech Mythos 4 speakers, so what don't you like about the Def Tech Mythos 4 speakers? (Please be detailed and specific.)
What exactly are your sonic (not musical) priorities? (volume, detail, bass, pin-point imaging, large soundstage, dynamics, smoothness, sparkling highs, etc.)
Do you already have a subwoofer? (I'd guess yes because the Def Tech Mythos 4 speakers are floor-standing they have average efficiency - 87.5 dB/w/m and roll off at 150 Hz so stand-mounted speakers should work for you that would provide more quality for the given budget.)