@cooper52 I have an suggested experiment that you could try. Your integrated has both pre-outs and HT-bypass. So, you could send the signal from the integrated’s pre-outs to an active crossover, then at the crossover, fork the signal, sending the higher frequencies back to the integrated’s power amp (via HT-bypass) and the lower frequencies to your subwoofer.
Options for your crossover include Sublime Acoustic’s K231, maybe a MiniDSP, or a JL sub crossover.
My experience. I’ve heard a JL crossover + subs in a buddy’s system. I think it sounded great. I haven’t heard the Sublime unit--I’ve only seen OCD Mikey recommend it on his channel as a solid contender for the money.
I’ve done what your describing with my TV system. In my TV system, I currently use KEF LS50 Wireless II’s, which have their own internal DSP engine with both high and low pass filters. I paired them with a REL HT sub. I had initially tried the crossover at the speaker’s -3db point (45hz) and at 70-80hz (often recommended in HT situations). I left the crossover at 80hz to live with for a while. Then, one day, I found someone’s charts showing when the LS50 speakers distorted across the frequency spectrum and at different volumes. I don’t recall the exact chart figures, but each chart showed distortion across the frequency spectrum when playing the speaker at different volumes like 80db, 85, 90, 95, 100, 105. What I saw in these charts was that starting at some volume, say 90db, that all frequencies 100hz and below were above some distortion percentage while frequencies above 100hz were not distorting. Charts at higher volumes saw a greater distortion asymmetry across the frequency spectrum. From that information I hypothesized that I should try handing off all frequencies below 100hz to the sub to see if I noticed any change in the sound. I went into the KEF software and changed the crossover to 100hz, and even though I wasn’t listening at 90db, the system sounded more effortless. (I also tried setting the Xover to 120hz, and that sounded equally effortless to me.)
Still today, I have this hypothesis that (1) some systems can benefit when offloading frequencies to subs typically handled by the speakers, that (2) crossing the subs over higher than usual (higher than 80hz) can be effective, and that (3) that a good setting for the crossover is the point where your specific speakers begin to distort asymmetrically across the frequency spectrum.
If you get into JL’s sub integration philosophy, you’ll learn that they’re big proponents of offloading low frequencies from the mains, and of crossing over at higher frequencies, even for expensive speakers that are "made to play full range." But, I haven’t seen JL articulate where to set a crossover at. Anyway, audio is an experiment, and in experimenting with this philosophy, you may find a solution that works for you.