SWAP/FIO

We have read precious little sleep and are most interested in trying FIO for 11 week old to work on independent sleep (currently rock to sleep and transfer).

When they awake for overnight feeding and go back to bed (usually 3/4am) how do I do FIO when they sleep in same room as my husband and I? Place in crib and then lay in bed while they fuss/cry in the intervals since we can’t leave the room? Or put them back down to sleep like I am now and wait until bedtime independent sleep is mastered and then do it for the night waking?