[Slakah]

My frame has no defining attributes at all, and isn't a child of anything

If you know when it's created you can find it.

also you can still find frames with no parents via EnumerateFrames().

What I use in StatusQuo:

local lastframe -- the last frame we met.
local otype
local function TextureStatusBars(f)
    local f = EnumerateFrames(f)
    while f do
        otype = f:GetObjectType()
        if otype ~= "Button" then
            if otype == "StatusBar" then
                SetTexture(f)
                f.SetStatusBarTexture = dummy
            end
            lastframe = f
        end
        f = EnumerateFrames(f)
    end
end
 
local function TextureNewStatusBars()
    TextureStatusBars(lastframe)
end