There is nothing wrong with moving on from Muzdalifah to Makkah straight away in order to do tawaaf al-ifaadah

Yes, it is permissible for the one who leaves Muzdalifah to go to Makkah straight away, and do tawaaf and saa’i, and come back, because the Prophet (peace and blessings of Allah be upon him) was not asked about anything that had been in a different order, but he said, “Do it, and there is nothing wrong with it.” So the matter is broad in scope, praise be to Allah, and Allah has made it broad in scope so that it will be easier for them. End quote.