I would be up the front with the baby for most of the Mass. If I’d had to take her out, the priest would usually remember to save me communion for when I got back. I agree with RedSoxWife that a baby who is already crying would often be calmed by the walk up the aisle.
I received on the hand with a small baby (because you can easily shift them up to have both hands free), but on the tongue when she got bigger and now, on the days when she is in the mood to walk calmly next to me, back in the hand. I’ve taken 2 children before and held one in each arm to receive on the tongue, obviously no chalice! Or I’ve had DD in a sling and her friend in my arms, that worked fine.
If you and your husband are both at Mass, would it be possible for one of you to take the non-crying baby to communion at the head of the queue, then return and take the crying baby whilst the other partner is still in time to join the back of the queue for communion?
Otherwise, as you said, you could wait at the back for someone to come to you, but you might need to be proactive about that, e.g. speak to the priest and indicate that you would like for it to happen.