Placing a hat on a character using a GUI with FilteringEnabled?

I'm creating a character customization menu for a custom player rig that's been rigged correctly and works swell. Upon the click of a button in a GUI, a hat is supposed to be cloned from a part and be given a mesh from a group called "meshes" in the lighting. The mesh applies to the hat just fine, and the hat spawns in, but it's supposed to parented to the player character. Instead, the hat spawns above the player and just falls onto the ground, unable to be picked up. I'm confused. The work is shown below.

function click()
    local player = game.Players.LocalPlayer
    local playername = player.Name
    local character = game.Workspace:FindFirstChild(playername)
    local children = character:GetChildren()

    -- This is where I spawn the hat.

    local hat3 = Instance.new("Hat")
    local part3 = Instance.new("Part")
    hat3.Name = "normalhair"
    part3.Parent = hat3
    part3.Position = character:FindFirstChild("Head").Position
    part3.Name = "Handle"
    part3.formFactor = 0
    part3.Size = Vector3.new(1, 1, 1)
    part3.BottomSurface = 0 
    part3.TopSurface = 0 
    part3.Transparency= 0
    part3.Locked = true 
    game.Lighting.meshes.normalhair:Clone().Parent = part3
    hat3.Parent = character
    hat3.AttachmentPos = Vector3.new(0, 0.15, -0.08)
end

script.Parent.MouseButton1Click:connect(click)