My integrated has only one set of speaker taps. Is ok to connect the converters wires to the same speaker terminals that are driving your main speakers?
That’s how I connected mine. I use banna plugs for the sub and raw wire for the speakers. I actually think the slight impendence change the sub adds helps the overall sound.
Record outs are fixed output so the volume of the sub will stay the same indipendent of the volume of the music... not reallly what you want. Speaker to line level adapters are really inexpensive and worth a try before you sell your sub.