If your (P) ticket was issued by QR you will not get into any lounges using your ticket.

There are no alternative ways in to Al Mourjan for those not holding a qualifying ticket, other than paying.

OWS will grant you and a guest access to the gold lounges. These may be the best for showers, subject to demand at the time.

PP will grant you access to Al Maha. Sleep n Fly is more like a short time capsule hotel than a lounge.

If you don't want to pay, the gold/platinum lounge at the north node is probably your best bet