Is it permissible for an engaged couple—after the marriage contract (Aqid al-Qiran) but before the wedding (Zafaf)—to physically enjoy each other, given the fear of the contract being annulled and the potential negative feelings this might leave the girl with, as well as the difficulty of expediting the marriage?

What you read, that the wife becomes lawful religiously after the marriage contract, is correct. However, if what the husband desires goes against custom, he must be patient and practice chastity until consummation. He can be aided in this by frequent fasting, guarding his hearing and sight, staying away from places of temptation, avoiding what arouses desire, and occupying his time with beneficial deeds, while seeking Allah's help and engaging frequently in remembrance (dhikr) and supplication (du'a).