Not only are they overpriced, they are underperforming as well (forget mesh). See the recent thread on that topic.
http://www.snbforums.com/threads/ho...his-summer-from-eero.22549/page-4#post-239650
The reading from post 70 on is worth the time.
With your wired rooms, I would be looking to put your main router in the most central position possible (if possible). The 'if possible' part is the ability to run several more cables (at least one each for each LAN port of your router).
Where the wires are terminated now, you need a switch (minimum number of ports equal to how many cables have been run to the rooms).
If you wanted to segregate your devices by switches, then you would have a switch for each LAN port of your router (hence the need for multiple runs to the (central) location where the main router was located).
The cautions about testing the cable runs and terminations (and the possibility of data not supported because of limitations of those aspects) would make me want to run new cables if possible.
If not possible? Then you have a very long road ahead of you testing each run and termination to make sure it adheres properly to data wiring standards.
I think that using the existing wiring (and forced to putting the main router there) is not a good exercise in the long run. Better to plan it out better and do it right before you start installing, buying and getting locked in to a sub optimal setup like you're faced with now.