From closed issue, this one is really needed. Any idea where to start looking? Guess it has something to do with HUD Stratum?

Yup. If you want to move nameplate over the top of every other nameplate, you have to destroy it and create new in different stratum F:API_GetStratum or you can use nil as a stratum (highest possible). Maybe there is a method to change parent of window but I haven't find it yet.