Subwoofer Connection: Speaker Level Amp to Line Level on Sub?

TAPE OUT or REC OUT take the signal before it's attenuated.  Tape recorders are built to handle this; not so much subs.  Which is why some preamps and some integrateds have more than one pair of PRE OUTs.

Hook wire from the speaker terminals to the Russound line level adapter to RCA’s to your sub. Crank that thing until you shake the house. This Russound is just like what’s found inside the Rel subs that are loved for this feature. Pump up the volume, dance. Enjoy.

This:

It should be fine if you connect the sub line level rca inputs to your amp speaker blinding posts via a LOC (line output converter). 

https://images.crutchfieldonline.com/ImageHandler/trim/1736/1129/products/2008/543/x543ADP12-f.jpeg

Oh dear, sorry to make that mistake, thanks for correcting me.

summadoggie, all you need to do is get a proper 2 way crossover. MiniDSP makes one which is very inexpensive.