You can't buy cards? OK, following alll of the new constraints:
Starting hand: King's Court, Throne Room, Workshop, Feast, Watchtower
Throne Room King's Court, KC Feast and Workshop.
With the KC'd Feast, gain 1 Feast and 2 Duchy. With the KC'd Workshop, take 3 Estate. Trash every card gained with Watchtower except for a single Feast. You will be trashing 6 cards each turn and draw the same starting hand each time. When the Estates run out, go for Feast instead.
Sample:
1: Gain and trash 2 Duchy, 1 Feast, 3 Estate
remaining: 6 Duchy, 5 Estate 8 Feast - note that there are 10 Feast total, 1 was in starting hand and 1 was gained.
2: Gain and trash 2 Duchy, 1 Feast, 3 Estate
remaining: D duchy, 2 Estate, 7 Feast
3: Gain and trash 2 Duchy, 2 Feast, 2 Estate
remaining: 2 Duchy, 0 Estate, 5 Feast
4: Gain and trash 2 Duchy, 4 Feast
remaining: 0 Duchy, 0 Estate, 1 Feast
5: Gain last Feast (trashing is optional)
remaining: 0 Duchy, 0 Estate, 0 Feast
3-pile ending thus achieved in 5 turns.
It could probably be done faster by gaining and keeping some throne rooms and more feasts and Workshops along with some drawing card to draw the entire deck, but I don't want to work it out without perfect shuffle luck.