woofers canceling each other

What Dave said. It could be one of the amplifiers inverts phase. The spec sheet for the amp should mention that. To test the phase of the speaker connecting a 1.5 volt battery to a speaker will show you if one of the speaker crossovers is inverting phase. Plus to Plus, Minus to minus. The woofer should push outward for positive phase by convention.
 
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What kind of terminals do those cabinets have?

If the common side by side spring loaded finger push or screw press type for bare cable ends, you can simply invert cable position (black to former red, red to former black) on one cabinet and retest.

That said, it´s kind of weird using different amplifiers for each channel, at least in Home/HiFi ; if anything because it´s hard to have them perfectly symmetrical to keep proper Stereo imaging.

On the contrary, very common in large PA installations, where multiple amps, quite often from different brands and models, are used together to power large banks of speakers.
 
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If you can play a pulse through the system from a test CD or app, there's probably some phone app that can detect the phase. It's probably a sensible thing to check anytime you have a mix of amps and speakers and processors in a system. (Elektor magazine published plans for a device pair back in Dec 1990, and reprinted it in a book of audio projects.)
 
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