Nighthawk X6 Tri-Band WiFi Router R8000 + 3 additional EX8000 – AC3000 Nighthawk X6S Mesh exted

What I'd try doing? 

connect the 2x EX8000's in the home with them setup in extender mode and not hardwired in. (with the "onewifi" feature enabled)  In extender mode, it still uses the smart roaming protocol so devices should work fairly well.You can also setup the EX8000's for different backhauls on the r8000. Meaning you could have one connected to the high band and the other to the lower band channels (might take some playing around with to get working like that).

You're garden one is the challenge. When the EX8000 is hardwired in, its ran in access point mode. Access point mode disables the roaming protocols. But most newer devices have their own smart roaming protocols built into them. So when you leave the garden shed, its structure could cause the device to automatically roam because of the decreased signal. So potentially you can have it with the same ssid as the house and potentially roam. It isn't as seamless as using a system like orbi or the MK nighthawk that supports both wired and wireless backhaul but it might work. 

That size of home should only need the router and maybe 1 extender, 2 max. 

You'll need to ensure the distance between the router and the 1st extender is in good placement and distance from each other taking into consideration the building materials. If buiding materials are causing some issues, try moving the 1 closest extender a bit closer to the router. say 5 feet+-. Check the extenders web page for status. If you see amber or orange connetion between it and the router, means that the connection is poor and may not work well. Should be green mostly. 

If you seem to find that signal isn't good, you may want to consider getting some LAN cable installed and connect a extender via ethernet cable to the router if the building materials are impacting the singles too much.