I have had birds with balance issues during a hard moult, and your question brought to mind a bit I noted from Jenni and Winkler chap 3 sect 4: "birds normally do 'nothing else' or are unable to do 'anything else' during a fairly rapid moult. In turn, this relative inactivity during moult is probably caused by the many non-energetic costs of moult, such as impaired flight, greatly reduced maximum oxygen consumption and impaired plumage function (waterproofing, display, insulation etc.), all with potentially negative consequences for survival." There's a lot going on beneath the hood, so to speak: moult is not just about feathers. So I wouldn't worry for now and just keep on with the tlc.