We have the little Avent cups as well with the screw on lids and I found them fabulous! We used to just send ours to DC frozen and then they would slowly defrost in the fridge then be transferred to her bottles, which were the tomme tippee closer to nature bottles so quite a wide top, that even it is wasn't complete defrosted before warming in a jug of warm water the milk would easily fit in.

I preferred them over the milk bags as they were reusable and were a lot cheaper to wash then replacing the bags all the time, and they stacked nicely in the freezer or fridge