Error 1012 persists after reinstall

[Triston]

After installing patch 3.22, I successfully played the game for one day. The next day, attempting to log in gives me the error 1012 when attempting to connect to the data center. I have attempted the following to resolve the issue:
* Restarting my computer
* Restarting my modem
* Restarting my router
* Uninstalling and reinstalling FFXIV
* Forwarding ports
* Temporarily disabling antivirus and firewall
I contacted Live Assistance technical support, and they suggested my ISP may have packet loss issues. I contacted my ISP (Cox) who reported no exceptional packet loss or ping issues. I successfully ran traceroutes to the Lobby server (199.91.189.74) which indicated no packet loss or ping problems at any hops.
I ran a 1300-packet pingtest, excerpt below:

Reply from 199.91.189.74: bytes=32 time=44ms TTL=52
Reply from 199.91.189.74: bytes=32 time=44ms TTL=52
Reply from 199.91.189.74: bytes=32 time=49ms TTL=52
Reply from 199.91.189.74: bytes=32 time=45ms TTL=52
Reply from 199.91.189.74: bytes=32 time=45ms TTL=52
Reply from 199.91.189.74: bytes=32 time=45ms TTL=52
Reply from 199.91.189.74: bytes=32 time=47ms TTL=52
Reply from 199.91.189.74: bytes=32 time=46ms TTL=52
Reply from 199.91.189.74: bytes=32 time=49ms TTL=52

Ping statistics for 199.91.189.74:
Packets: Sent = 1312, Received = 1312, Lost = 0 (0% loss),
Approximate round trip times in milli-seconds:
Minimum = 44ms, Maximum = 67ms, Average = 45ms


No packet loss at all, excellent ping.



-=-=-=-=-=-=- FFXIV Information -=-=-=-=-=-=-

MyDocument C:\Users\\Documents
FINAL FANTASY XIV - A Realm Reborn D:\Program Files (x86)\SquareEnix
FINAL FANTASY XIV - A Realm Reborn Language 1 Region 2
ProxyEnable 0
ProxyServer 124.41.94.210:3128
ProxyOverride 127.0.0.1:9421;<local>


-=-=-=-=-=-=- System Information -=-=-=-=-=-=-

SYSTEM_OS Windows 7 Home Premium 64-bit (6.1, Build 7601) Service Pack 1 (7601.win7sp1_gdr.160211-0600)
SYSTEM_CPU Intel(R) Core(TM) i7-2630QM CPU @ 2.00GHz (8 CPUs), ~2.0GHz
SYSTEM_CORE_NUM SYSTEM_CORE_LOGIC 8 SYSTEM_CORE_PHYSICS 4
SYSTEM_BIOS BIOS Date: 04/27/11 14:06:47 Ver: 04.06.03
SYSTEM_LANGUAGE English (Regional Setting: English)
SYSTEM_MEMORY 8169.180MB
SYSTEM_VIRTUAL_MEMORY 2047.875MB
SYSTEM_PAGE_FILE 16336.566MB
SYSTEM_STORAGE C:\ SYSTEM_HARDDISK_DRIVE SYSTEM_TOTALDISC_SPACE 440.760GB SYSTEM_FREEDISC_SPACE 41.749GB
SYSTEM_STORAGE D:\ SYSTEM_HARDDISK_DRIVE SYSTEM_TOTALDISC_SPACE 1863.009GB SYSTEM_FREEDISC_SPACE 1207.396GB
SYSTEM_STORAGE Q:\ SYSTEM_HARDDISK_DRIVE SYSTEM_TOTALDISC_SPACE 1863.009GB SYSTEM_FREEDISC_SPACE 1207.396GB
SYSTEM_DIRECTX_VERSION DirectX 11
SYSTEM_GRAPHICS NVIDIA GeForce GTX 560M
SYSTEM_GRAPHICS_DEVICE \\.\DISPLAY1
SYSTEM_GRAPHICS_CHIP GeForce GTX 560M
SYSTEM_GRAPHICS_MAKER NVIDIA
SYSTEM_GRAPHICS_VRAM 2000.438 MB
SYSTEM_GRAPHICS_SHARED_VRAM 2047.887 MB
SYSTEM_GRAPHICS_DAC Integrated RAMDAC
SYSTEM_GRAPHICS_DISPLAY_MODE 1600 x 900 (32 bit) (60Hz)
SYSTEM_GRAPHICS_DRIVER nvd3dumx.dll,nvwgf2umx.dll,nvwgf2umx.dll,nvd3dum,nvwgf2um,nvwgf2um
SYSTEM_GRAPHICS_DRIVER_VERSION 10.18.0013.5330
SYSTEM_GRAPHICS_DRIVER_DATE 6/17/2015 5:10:27 AM
SYSTEM_GRAPHICS_DRIVER_LANGUAGE English
3.0
SYSTEM_GRAPHICS_PIXEL_SHADER 3.0
SYSTEM_GRAPHICS_VERTEX_TEXTURE SYSTEM_SUPPORT
SYSTEM_SOUND Speakers (Realtek High Definition Audio)
SYSTEM_SOUND_DEVICE_ID {B205FAC2-A952-4727-9BB4-08E34B9B0E3A}
SYSTEM_SOUND_DEVICE_NAME RTKVHD64.sys
SYSTEM_SOUND_DRIVER_VERSION 6.00.0001.6564
SYSTEM_SOUND_DRIVER_LANGUAGE English
SYSTEM_SOUND_DRIVER_DATE 2/6/2012 6:41:14 PM
SYSTEM_INPUT {6F1D2B60-D5A0-11CF-BFC7444553540000}
SYSTEM_INPUT_NAME Mouse
SYSTEM_INPUT_REMARKS SYSTEM_GAMEPAD_AXIS 3 SYSTEM_GAMEPAD_BUTTON 8 SYSTEM_GAMEPAD_FOV 0
SYSTEM_INPUT {6F1D2B61-D5A0-11CF-BFC7444553540000}
SYSTEM_INPUT_NAME Keyboard
SYSTEM_INPUT_REMARKS SYSTEM_GAMEPAD_AXIS 0 SYSTEM_GAMEPAD_BUTTON 128 SYSTEM_GAMEPAD_FOV 0

-=-=-=-=-=-=- Proccess Information -=-=-=-=-=-=-

C:\Program Files (x86)\ASUS\ATK Package\ATKOSD2\ATKOSD2.exe 000007F4
C:\Program Files (x86)\ASUS\Wireless Console 3\wcourier.exe 0000101C
C:\Program Files (x86)\NVIDIA Corporation\Update Core\NvBackend.exe 00000FB4
C:\Program Files (x86)\Panda Security\Panda Security Protection\PSUAMain.exe 0000106C
C:\Program Files (x86)\Skype\Phone\Skype.exe 00000BAC
C:\Program Files (x86)\Spybot - Search & Destroy 2\SDTray.exe 0000103C
D:\Program Files (x86)\SquareEnix\FINAL FANTASY XIV - A Realm Reborn\boot\ffxivsysinfo.exe 000015AC


I am completely tapped out of ideas; how do I resolve this?

[Triston]

Speaking with Live Assistance tech support again, the problem seems to be that Square Enix's servers, on attempting to ping my public IP, fail a connection test at my ISP's server. Speaking to my ISP, they report no issues with the relevant servers, and are able to ping my IP successfully.
I don't know enough about networking to determine why Square Enix specifically is unable to connect to me, even though I can successfully connect to them.