For general background listening, I prefer a few more speakers, rather than a few less. I run two sets in my kitchen/eat in space in my home and it provides very nice coverage. I don't plate them close, like you're showing in your second photo. Instead, I would spread them out more and center them in the space. This isn't so much about proper stereo, as it is about even coverage throughout the space with decent sound. So, I'd put one on either end of the dining room table and one on either end of the island area. This will give you general 'centered' sound throughout the space.
I lean more towards picking up a main brand used amplifier off of eBay vs. cheap stuff on Amazon. Lots of decent reviews of the amp you're considering, so I'm not going to tell you not to get it, but be aware, for the money, you could likely get a Sonance 260 or 275 amplifier used. Niles and Speakercraft are other popular makes for distributed audio amps that work well and hold up for decades. I use Rotel stuff for my distributed audio. Be aware, the amp you are considering
Grey structure rate with labour does not include a power supply it seems, so that will be an additional purchase/cost.