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 It needs organic matter and time. This might be a good case for using raised beds, though.  
 All mine so far are raised or no till. Trying to get some trees in the ground  
 It's going to be hard to get trees growing unless you go from seed & then you get a lot of variability. 

Comfrey is your friend & doesn't generally compete with trees. It'll send a nice big tap root down into the clay & encourages soil life (they drop a lot of exudates). You gotta keep that clay moist with mulch though.

With your lasagne bed construction, lay some crushed charcoal (bio char) down at the soil layer. As this gets incorporated into the clay, it'll improve drainage & soil life.

Use fast growing support trees like eucalyptus & legume trees to eventually pollard & coppice for bio mass.

Clay is nutritious & holds water/life if it's kept moist. Drainage & compaction (no air pockets) is probably your biggest issue with it. Keep piling on organic matter that will be incorporated by the soil life you'll encourage.