Slinki minki fleece pockets might be good for you. they are velcro so v quick to put on. They are v cheap preloved but they usually dont come with an insert. The pocket is huge, u could stuff a house in there.
They do give a big bum look but are v reliable and once stuffed go on in one piece which is great with a wriggling baby, i even manage to put them on with DD standing up sometimes if she is being particularly difficult