Okay, I think I found the problem.
Archy is hard coding the position relative point to the UIParent regardless of what you parent the frame to. Understandable if you assume it isn't going to be hooked into an interface but it means that there is no way that I can see to override it without rewriting the Archy function itself which seems to work so far.
So far, making a copy of the SetFramePosition function of the original Archy addon and replacing the digsite positioning code seems to be enough for now but being at a low stage in the profession perhaps you can see how it works as the list grows as even now it hooks just over the bottom of the frame.
Anyway, here's the latest copy of the code with the above change implemented so that you can see how it works for you. Where it may possibly override your original archy settings I would suggest at least during testing that you make a copy of your existing Archy wtf files so as to keep the current positioning data intact so that you can fall back to it at a later date as needed.
If it does indeed seem to work for you okay in its current state then I will see if I can hook the saving position data function and implant an nUI specific version so that it never overrides the data so that the user can remove the plugin and not notice the difference