Creating a "mesh" WiFi network via hardwired cables
I am trying to figure out how to reconfigure my existing WiFi network such that I can move between my house, my barn, and my garage without having to keep disconnecting and reconnecting to different SSID names. These three structures are all connected by 1Gb cable, and currently, I have my tp-link Archer A7 in the house directly wired to separate access points in each remote structure, each with a different SSID. The structures are each maybe 200' or 300' from the house, but in different directions. I tried a WiFi extender in the barn once, but it wouldn't stay connected to the router in the house, since the signal from the house was very weak in the barn.
A) Is it possible to just use the same SSID for all three WiFi areas, so that when I walk from the house to the barn, my phone will stay connected and automatically switch to the closest (strongest) network? If so, what are the rules for setting this up (same or different channels, etc.)? Is this the best way, or not a good idea?
B) If I decided to go with the new Mesh technology, does that even work for my situation where the two remote mesh devices would have to be connected via cables to the main router instead of wirelessly? Is this a better solution than Option A) above, or are they equivalent? I realize I would need to replace my main router with one that supports Mesh, since my A7 apparently does not, and also buy new Mesh access points to do this. Would I need a certain type of remote Mesh device to use the cable from the main router?
Is there another solution that would be better for this situation?
I would greatly appreciate any advice. Thanks!