variation of thickness of dielectric layer for different textile-based capacitive pressure sensors
The capacitance of a parallel plate capacitor is given by

$$ C = \kappa \epsilon_0 \frac {A}{d}$$

where \$ \kappa \$ is the dielectric constant, \$ \epsilon \$ is the permittivity of free space,  8.85 × 10−12 F/m, A is the area and d is the distance between the plates. Here we'll be using metric measurements rather than the quaint inches.

Checking your calculations for your 3" x 3" at 900 µm capactior with 3.4 dielectric we get

$$ C_{900} = 3.4 \times 8.85 \times 10^{-12} \frac {0.0762^2}{900 \times 10^{-6}} =  1.88 \times 10^{-10} = 194 \ \text {pF}$$

If we decrease \$ d\$ from 900 µm to 400 µm the formula says that the capacance should increase by \$ \frac {9}{4} \$. Checking this we get \$ C_{400} = 188 \frac {9}{4} = 436.5 \ \text {pF}\$. 

So your calculations are confirmed. Back to your question ...


  Is that going to be way too much variation or is that relatively close enough?


Only you can decide that. If you can tolerate a \$ \frac {9}{4} \$ variation then yes, otherwise no. I suspect not.