[Fizzlemizz]

Once you have the frame (bubbleframe here) you can use:

for i = 1, select("#", bubbleframe:GetRegions()) do
    local region = select(i, bubbleframe:GetRegions())
    if region:GetObjectType() == "FontString" then
        region:SetShadowOffset(2, -2)
    end
end

Personally I can't figure out when/why the system will use protected chat bubble frames or not.