Bose HU pushes full range balanced line-level signal to the amp so you can't just connect a RCA plug to it.
Is it possible to use this product to convert balanced signal to unbalanced signal?
Amazon.com: MCM Custom Audio 555-8485 Balanced / Unbalanced Line Level Converter: Everything Else - $50
It uses 12 VDC so powering it is no problem. If this worked, it seems like a CHEAPER and BETTER solution than a sound processor like LC7i, or cleansweep. Because you are cutting down the "processing" part and getting clean and flat signal directly from the HU.