AV Receiver with Integrated Amp - Sub Connections?

Here’s the best solution Integrated Amp available on the market (link below)...Might make you want abandon the surround sound receiver, center and rears you have and convert movie watching to stereo with a sub.  
Or, you can upgrade from your receiver/integrated combo to a better overall receiver or go to a separate pre/pro and power amps.
https://www.anthemav.com/products-current/model=str-integrated-amplifier/page=overview 

And DOES HAVE Home Theater Bypass FYI...

I think I get what you want to do because I’m planning at some point to do something similar. It blows my mind that a lot of companies have “home theater” pass throughs but never do they have sub inputs and outputs which is nuts as subs are critical to home theater. Maybe they assume you won’t be using subs for two channel which I think is also silly.  Take a look at the JL Audio cr-1 crossover and see if that does what you need. 

My NHT SubOne i has an external controller that has inputs for both LFE and Audio. You can connect the receiver via the LFE/subwoofer output and you can connect an integrated amp, or pre-amp, via an analog line-level output. You can set up each connection independently. I don't know if there are any other subs that have this option. Perhaps there are some subwoofer controller that offer this type of connection.

If you end up looking for a more adaptable sub...

Please check out:

https://youtu.be/tJJtWokUIWk

https://www.paradigm.com/en/ported

These have speaker-level inputs as well!