UA Mileage Plus 50K would help you. The time is tight but possible. Apply now, get the card, activate it and ask for closing cycle date. Typically, miles are posted on that day or sometimes 1 or 2 days later. Since you have Chase SP, transfer points to UA now and book 1 way trip first.
The transfer would take instantly. I do not know your return date. If it is too close to the departure date, might not possible to have cheap ticket for low miles. Good luck