The PAC ROEM-NIS2 Wiring Interface, the same one I installed in my '02, retains the function of the factory Bose amplifier and allows the factory speakers to be used. It is not a bypass. It is a system integration adapter. Without it, the factory 2 ohm speakers would draw too much power from your new head unit and wreck it. The Boss BE7ACP-SD, like most every other newer audio system, functions with 4 to 8 ohm speakers and cannot have 1 to 2 ohm speakers connected directly to the head unit .
From what you said about this new Boss system acting just like the last 2 old Bose head units, my best guess is that your Bose amplifier is toast. Wish I could tell you how to bench test it to be sure but all I got is my best guess on this one.
The Bose amplifier can be bypassed but you will have to replace the 4 speakers in the doors and the 2 tweeters in the front pillars. The Boss unit you have has a built-in internal amp (20 watts RMS/85 peak x 4 channels). Nothing stellar but it would be an massive improvement over what you have going on. To do this, the PAC wiring interface would have to be removed. The bypass can be done different ways. This link takes you to one way I have seen that does not involve extensive work but it is no walk in the park either.
https://themochinist.tumblr.com/post/12 ... a**-if-you
If you can find a functioning Bose amplifier to replace your old one, that would be the easiest thing to do. They are all over e-bay for about $50.
https://www.ebay.com/itm/294239484682