I think I'll wait rather than pay £160 for a new screen as I've already bought a new phone.
Which phone you have right now? £160 to just change your screen sound quite high.
Anyway if you are willing to than you can wait for response from poloniex support. I have also enabled 2FA there but I have made a copy of my recovery words to access my account if I get into similar problem. Next time, don't forget to make proper backup.