I got it to work.
The issue is confirmed to be caused by loading any ISO file. I must load the game through a physical disk of the game.
1. Downloaded the latest SVN.
2. Extracted it to a folder in My Documents.
3. Deleted portable.ini, placed my bios in the root. (I did NOT change the path to the bios folder in my documents)
4. Opened up the PCSX2 folder in My Documents. Deleted the ini folder just for good measure.
5. Ran pcsx2-r5731.exe as administrator.
6. Error thrown that there was no config for my GPU plugin. Configured plugins by just changing the DEV9 to devnull plugin (otherwise, I crashed). Did NOT mess around in the GPU plugin configs. Just left it as Gsdx32-AVX-r5727. All I set in that plugin's options were to point it to my Nvidia GPU and to DirectX 11 Hardware.
7. Put in my physical disk of Syphon Filter: The Omega Strain (no ISO mounting, not loading an ISO file...)
8. Directed the DVD plugin to E:/, where my game disk was located.
9. Boot (Full)
Out of pure curiosity, I tried selecting my ISO file I ripped from this very disk a couple years back, and the problem WAS THE ISO. It works on my other computers, yet if I try and load any ISO into my emulator, it hangs!
I'm posting this so coders and devs can see what my issue was and see if they want to add this to some kind of known bug list, or some kind of "known workarounds" list. If this issue happens to someone, try popping in a disk to the disk drive (maybe mount the ISO virtually if they lack the disk drive) and using the plugin "cdvdGigaherz-r5692" worked for me.
Here's proof it works: