Edinburgh is best in May or September when the crowds thin out and the city feels like your own. Walking the Royal Mile and exploring the castle ruins is cheaper and much more pleasant when you aren't fighting the summer rush.
You can manage the $2800 cost by using the Discover it® Cash Back card. It offers 0% intro APR for 15 months on purchases and balance transfers, which lets you pay off the trip over more than a year without interest charges.
The 0% intro APR is a deadline, not a gift. If you still have a balance after 15 months, the card will charge interest on what remains, so make sure to finish your payments before the window closes.