If you want to go full OCD, don't assume anything about the speakers. Trust, but verify.
Push on connectors are bad. Soldered connections better.
Anything magnetic at the binding post, replace.
Picture of the crossover indicates both good and questionable. Several good quality components, but far from better that could have been included for the price of the speaker. Impossible to tell for sure, but possibly a couple small electrolytic caps near the large inductor. Bad. Sand cast resistors. Bad.
Mention of 5th and 6 order filters begs the question - Why? That level of complexity indicates significant compensation required for correction of a problem. Driver response, phase, breakup, resonance, cabinet?
If there is in your opinion an issue is sound quality, proceed at your own risk.