Is refusing to write the deferred dowry (Mahr مؤجل) in the marriage contract and sufficing with the advanced dowry (Mahr مقدم) considered a violation of the Sunnah or scholarly consensus, or is it permissible and from the Sunnah?

It is permissible for the dowry to be partly prompt and partly deferred. The fact that the Prophet, may Allah bless him and grant him peace, did not defer any part of the dowry does not mean that deferment is prohibited. If the girl's family desires to defer a portion of the dowry for her benefit, it is advisable to agree to that.