Switzerland is quietest in May or October, when the summer crowds have left and the first snow hasn't yet buried the trails. You get crisp mountain air and lower hotel rates, making it the perfect time to wander through Interlaken or ride the trains through the Bernese Oberland.
We can manage the $4500 cost by using the Citi Simplicity® Credit Card, which offers 0% for 18 months on purchases and balance transfers from date of account opening. This gives you an 18-month window to pay off the trip in manageable chunks.
Remember that the 18-month intro window is a deadline, not a gift. If you do not pay off the full $4500 balance before the window closes, the bank will start charging interest on whatever amount is left.