I put our Moses basket inside the bassinet for the exact same reason, and we did this until he grew out of the basket. By this time, the bassinet didn’t seem to scarily big and he didn’t notice the transition :)
Swaddle is your best bet, this way she is held in a nice hold no matter where she sleeps. It helps with the startle reflex. Also pop your Moses into your next to me this might help
Unpopular opinion but get a purflo or sleepyhead in her next 2 me x
Pop her basket in the crib! As she gets older you can transition the basket out 😊
Babies have something called a ‘startle reflex’ that is what’s happening when she’s being led down. Swaddling should really help with this! You can swaddle until baby shows signs of rolling and then they need to be transitioned out of the swaddle! You can also try putting her into the bassinet slowly, bum first and then slowly lowering her head so it’s not such an instant shock, and then keeping your hand on her tummy!x