(FYI... he means that if you replace the OEM Bose, it has to be with the exact same one (year / vehicle.) The harness leads changed on the amps a few years after they started putting in the Bose components; then they went to a revised amp chassis, as well)
Double-check the connections, per your HU and the GMOS instructions, both for wire-wire function, as well as connectivity. If you weren't getting that cutting out before the GMOS, it's kinda 'beyond coincidence' that the amp would 'fail further' at the same time. Yes, the Bose amps do go bad, with age; I'm not defending them. You may have a short in one of the Bose amp leads, as well (power / ground / turn-on lead). Although you'd probably be blowing the amp fuse (in the fuse block) if this were true, especially if it's at the power or ground wires.
Further isolating things, you could attach a speaker to one of the HU outputs (assuming it has an internal amp of its own), verify that it's working OK, repeat for the other channels, then bring back the GMOS and test that. Don't forget to adjust your balance / fader controls when doing this; it's not good to drive disconnected outputs, especially at higher levels.
Also, speaking of fader / balance, the OEM head unit is supposed to have fader / balance centered, before you remove it and install the new HU and GMOS. Axxess does specify this (and I'll admit, I've forgotten about it myself.) Haven't noticed anything adverse when I didn't do this, but if they specifically advise to do this, it's worth following the instructions. (the potential problem is permanently out-of-sync levels, if it manifests itself)
Finally, if you do decide to replace the amp with an aftermarket (admittedly, the best long-term strategy, if you want more power than the amp in the HU can supply), you can swap out the GMOS-04 for a GMOS-01, which will still preserve chimes (comes with the outboard chime box), but not the amp leads (you'll be running new ones, anyway). Using a harness of some type will save you from having to cut the factory harness and potentially misidentifying the wiring / creating a mess to figure out. If you like / use OnStar, then I think you may need the GMOS-02. Verify this at Axxess' site (which is difficult to navigate / narrow down choices, for our older vehicles).
Don't forget that if you have steering wheel controls, and want to keep them, you'll also need the ASWC from Access, as well (it integrates with the GMOS, via a subharness)