There is nothing like fast or slow pilgrimage, rather the concern is on the accomplishment of the pillars in order to judge whether the Hajj is valid or not. As for acceptance, this needs sincerity after fulfilling the pillars and conditions of Hajj, which only Allah knows this.
Sheikh Dr. Yusef Al-Qaradawi says:
Hajj takes four days from a person. From the day of al-Tarwiyah, which is the eighth day of Dhu al-Hijjah, he goes and sleeps overnight in Mina. He prays five times daily prayers there. Then, on the ninth day, he goes to Arafat, and stands at the great position supplicating, remembering Allah, saying tahlil, glorifying (Takbeer), and praying until sunset.
Thereafter, he returns to Muzdalifah for stoning Jamarat al-Aqabah. After that, he circumambulates the house (of Allah) on the day of sacrifice, on the great day of Hajj. Also, he jogs between Safa and Marwah. Then he throws the ritual stones on the first, second, and third day. “And remember Allah during [specific] numbered days. Then whoever hastens [his departure] in two days – there is no sin upon him; and whoever delays [until the third] – there is no sin upon him – for him who fears Allah. And fear Allah and know that unto Him you will be gathered. [Quran 2 : 203 ].
On the third day of Eid, it is possible – as Imam Abu Hanifa says – to throw the stone from the morning on the day of Al-Nafr; to throw it and travel back to his country, thus marking the end of Hajj, and there is no blame on him after that.