@Hayabusa is correct in pointing out that you can get close to double the power with an active crossover. I saw you mention the miniDSP but did overlook that the passive crossovers can be defeated. Since this is a three way speaker, you would need to do some calculations (or tests) to determine how you divide the drivers and to see how much power you can gain.
Nonetheless, as mentioned by other fellow members, you typically need
a lot more power (4x +++) to get a noticeable gain in SPL and these speakers are not specified for that much more. So higher efficiency speakers would be the easier route. I would add that it's also not a given that you
need that much. Most people end up in the single digit Watts range at normal listening levels. The other stuff you mention with the HK receiver playing much louder also points to a
lack of gain in your regular setup and not a lack of power.