I had redeemed Skywards points for JetBlue a few weeks ago, for travel next month. This is how I would recommend going about it:
- Come up with a list of flight numbers and alternatives for the dates you would like to be booked on.
- Call Emirates (on their 1800 number from the US), and give them those flight numbers until you find one which is available.
You are charged per sector, so JFK-BOS-PIT cost me 9000+7500 miles. A little more than what I would have liked to spend, but the miles were expiring anyway.
Taxes and fees were around $16 per sector.
Additionally, try to get the agent to enter the TSA information online right after the booking is confirmed. I am having issues with that currently - JetBlue does not let you access the reservation online if the ticket is on Emirates stock, so you might have to call them for a confirmation as well.