In my opinion, swapping to the front speaker outputs will make everyone in the family happy. It should restore the CarPlay (and maybe a similar issue with BT that's yet to be found out) functionality and may also help with the overall sound. As for the speaker wires into the doors, considering you skills, amount of power, and overall expectations, I would find where the speaker wires go into the door (in the cabin side) and tap onto them there. There isn't necessarily a risk of fire or destruction with how you've got the wires run now, but you might have an issue down the road with amp if the wire insulation wears and starts to short out the amp.
Everything else looks good. Good luck with your search for bottom end. You might have some luck with deadening the doors but it will be time/labor intensive and adding the Bazooka may be cheaper and easier.