Attaching Accessories to morphs?

Hi, I am working on a role playing game which relies on morphs. Unfortunately many of these morphs don't comply with the height of a Robloxian head, so hat giver scripts will have the hat floating above the player by a significant amount.

I am trying to make some hats using the Accessory class that will attach using a weld to a specific brick in the morph called Attach. This way, I can modify where hats appear on each morph.

The script mostly works, so the hat is duplicated and put in the correct brick. My main problem is that I don't know how to make two Attachments (one in the Attach brick in the player, and the other created inside the new hat using a script, both are named AttachMe) become one Weld when using a giver script to put the hat into the body.

debounce = true

function onTouched(hit)
    if (hit.Parent:findFirstChild("Humanoid") ~= nil and debounce == true) then
        debounce = false
        local a = Instance.new("Accessory")
        local p = Instance.new("Part")
        local a2 = Instance.new("Attachment")
        a.Parent = hit.Parent.Chest1
        a.Name = "WizardHat"
        p.Parent = a
        a2.Parent = p
        a2.Name = "AttachMe"
        p.Position = hit.Parent.Chest1.Attach.Position
        p.Name = "Handle" 
        p.Anchored = false
        p.formFactor = 0
        p.Size = Vector3.new(5,4,2) 
        p.BottomSurface = 0 
        p.TopSurface = 0 
        p.Locked = true 
        script.Parent.Mesh:clone().Parent = p
        wait(5)
        debounce = true
    end
end

script.Parent.Touched:connect(onTouched)

The new hat just falls onto the ground and cannot be picked up. It's a child of the player model, but the Attachments don't connect.

Any advice will be much appreciated!!