But it does produce extra bass.
A full-range speaker doesn't have flat response below its spec, but it does have response. Your woofer will be moving with a 10hz signal, even DC if it's sent down the wire to the speaker.
If your subwoofer is crossed at 40hz, it will produce very little if any above 40hz, but from 40hz down the subwoofer and the main speakers are producing sound. Whether these sound waves coming from separate positions are in phase or not, will depend on many things including room acoustics and positioning. If you turn down the gain on the subwoofer so that you don't hear it you are defeating the purpose of having a subwoofer to some extent. You do not want the sub and main speakers competing.
You like the way your speakers sound compounding and/or cancelling below 40Hz? Nothing wrong with that, and the OP might like it also. My point is simply to point out how that isn't going to create a flat response curve, nor anything close. My suggestion is still to go speaker A out to sub high-level, sub out to main speakers. If the sub has a good crossover in it this should be the best result without buying additional equipment.
Another option would be to add a DSP, go preamp into DSP, use the DSP for your crossover, high-pass out to your main amp and main speakers, low-pass out to your subwoofer low-level in. This will allow you to tailor your crossover point and type to give you the most seamless transition between main and sub. You can buy a mini-DSP for around $100 and it will give you much flexibility.
Easy answer is: try it both ways, through the sub's internal crossover and with the two compounding below your crossover frequency. Neither one costs you anything but wire at this point, and you might find that you like it. Be aware that speaker (and especially subwoofer) placement will drastically affect sound levels, putting the sub in a corner will give you a lot more bass than out in the room, on the floor more than up off of the floor, etc. The bass isn't directional so placement isn't important for imaging, but putting it too far from the main speakers will affect the balance. Also, many subs have a phasing switch, try it inverted and normal to see which gives you more bass.