I was able to purchase my fluid locally from a hobby store many years ago. 100,000 cSt silicone fluid is easily obtained from the online from eBay sellers or even Amazon. Around $10 for 2 ounces. There is no audiophile brand.
Do you actually have a WTRP or a Classic turntable. The WTRP didn't come with a black damped platter. Is your tonearm a single post with the fluid cup attached directly to the post or is the cup attached to the bottom of a mounting plate with two uprights and a scale on the side to indicate adjusting VTA and tonearm height? If the latter, the arm has a vernier-shaped knob that is the anti-skate adjustment. The simplified arm on the WTRP does not have anti-shape adjustment. You would need to disconnect the attachment point for the monofilament and remove a possible half twist of the strings.
There needs to be enough fluid around the disc so the arm behaves like it's being held captive around the rotation axis of the tonearm. If the disc is just touching the fluid, the arm would have excessive movement, especially when cueing a disc. Adding additional fluid causes the arm to become more axial on it's rotation. But again, if you have too much fluid covering the disc, the arm will drift very slowly down because of the extra dampening. This will all reduce the overall noise and give a blacker black. The negative with too much dampening is a deadening of the dynamics of the music and loss of intimacy. The music will sounds a few rows back. With a cartridge like your Grado which are always voiced with mid range purity, the bass can sound out of balance with too much dampening.
Others will have their own opinions of how much fluid to use. I will add this. I own a prototype Well Tempered Arm mounted on a old AR XB turntable. This was the turntable that Bill Firebaugh left with the Southern California dealer to evaluate. I listened to this turntable set up for many months until it was available to purchase from the dealer. The disc was well covered by the silicone fluid. I still use this 35 year old arm and table in one my of systems daily. As well as an early WTRP.