The old solution to your quandary is to install a simple high-pass filter on the input jacks of the power amplifier driving the main speakers. A single capacitor and resistor creates a 1st-order filter that removes frequencies below a certain Hz at a rate of 6dB/octave, that Hz determined by the value of the cap and res in combination with the amp’s input impedance. That frees both the amp and speakers from having to reproduce low frequencies, which results in lower distortion and cleaner sound to higher SPL. Installing the filter on the amp’s input jacks removes the need for an extra set of interconnects.
A 1st-order filter does not remove bass from the main speakers and their amp to the same degree as does a higher-order filter, the 2nd, 3rd, and 4th-order (12, 18, and 24dB/octave) found in active electronic crossovers, but if you want to avoid such a x/o and the required extra set of interconnects, it’s the way to go. This has been done by DIYers since at least the 1950’s. The formula for determining the values of the cap and resistor required to create a 1st-order filter at any chosen "corner" frequency with any amplifier input impedance is all over the internet; a Google search will lead you to it.