Fight Night Round 3 and Prince of Persia trilogy just to name a few.

I think these games will fit the bill:

Ico

Final Fantasy X

Metal Gear Solid 3

Silent Hill 2, 3 and The Room

Prince of Persia series

Final Fantasy Tactics, 7 & 8 (if you don't already have these classics for the original PS)

Bully
Devil May Cry
Devil May Cry3
Final Fantasy X
Final Fantasy XII
God of War
God of War 2
Grand Theft Auto: III
Grand Theft Auto: Vice City
Grand Theft Auto: San Andreas
Grand Turismo 4
Guitar Hero
Guitar Hero 2
ICO
Killzone
Metal Gear Solid 2
Metal Gear Solid 3
Need for Speed: Carbon
Okami
Resident Evil 4
Shadow of the Colossus
Socom 3
Soul Calibur 3
Tekken 5
We Love Katamari

I'd recommend the following:

Prince of Persia trilogy

Godfather

Fight Night Round 3  

Call of Duty 3

Black

Legacy of Kain: Defiance

Silent Hill 2, 3, & Silent Hill: The Room

Splinter Cell series

Onimusha Warlords 1,2 & Dawn of Dreams

Ghost in the Shell: Stand Alone Complex

Tomb Raider Legend 

I got hooked with all these games and  some that you mentioned in your list. Enjoy!!! 

Square Soft came out with games like Final Fantasy 7 & 8, FF Tactics, Parasite Eve 1 & 2, Bushido Blade 1 & 2, Vagrant Story just to name a few in a span of 4 years or less on the PS console.

How many solid titles has Square Enix released? I think Square Enix still has some awesome titles under it's belt as we speak but none to match what Square did during the late 1990's and early 2000.