OP, I feel your pain, mini-FFJA is 4 weeks old today and has same thing with becoming unsettled when we decamp upstairs to bed…
+1 for strokes and head, gentle voice etc, midwife suggested that because our room is a bit cooler than living room (freezing old house with no central heating) to try popping a hot water bottle into basket to warm it before putting baby in. Obv take it out before you put them in!
Also, bottles and formula are life savers, don’t let folk tell you otherwise! Mrs FFJA struggled boob feeding and was in agony, (baby a bit tongue tied), formula saved her sanity!
All the best