LDO getting hot on short circuit somewhere between Eth socket and LDO - how to best identify the short circuit spot?
If the only parts that are getting hot are the LDO and the Marvel 88E1318 (Ethernet PHY) then it is probable that the PHY is faulty. If you have the tools then remove the PHY. While it is removed you could check for a short on Vout, you should find it has gone. You could also power up the board with the PHY removed and check Vout, it should now be 1.8V. Replace the PHY and hopefully the fault has gone!