You definitely can put a LUX system in a non-LUX vehicle, but as you are finding it does require some rewiring. It is not plug-and-play. I've done it, and I think the sound improvement is worth it. It looks like you have the amplifier wiring modifications, but to get the full benefit, you will need to run 4 new wires from the amp to the driver's kick panel. The rear door speakers and the D-pillar speakers are tied together at a connector there on non-LUX systems. To do it properly you will need the correct terminals to separate the wires and put the D-pillar speakers in their own cavities and connect the new wires to them. To really do it right, you will need terminals for the console harness connector under the cup holders. If you don't run the new speaker wires through that connector, you will have these speaker wires preventing you from removing the console.
Then, the amplifier needs to be configured to your cabin type (standard, XL or EXT, or if it's a Denali LUX amp it could even be configured for a standard pickup cabin). If you know what it came out of, it may already be configured for your cabin, but if it is not or you don't know what the donor vehicle was, then you'll need a Tech2 or a trip to the dealer to set it up properly. In my case, the D-pillar speakers had no output after I separated the wires until I programmed it for a standard cabin Escalade.