That is just not true. The Mayflower was a Dutch Fluyt which meant that it’s top speed was 8, maybe 9, knots with full sail and a favorable sea condition for short bursts, but more likely averaging about 4-5 knots in a full long haul cruise. The Triumph Mayflower has a posted top speed of 56.5 knots, and even if it only goes 40 knots in its full cruise, it is still ten times as fast as the Pilgrim Quitters’ ship.
Edit: Just a quick reminder, in principle, that the persecution the Pilgrims were fleeing in Europe and particularly England, was that they felt persecuted by not being allowed to force everyone else to worship like them. They were not prevented from worshipping how they saw fit, but were told they could not push it on others. It was the birth of the American persecution complex.