Let's assume you take a parallelepiped of pumice with vertical dimension h, width a and length c, and put it into water. To which extent will it sink? If we call the sinking s and indicate the density with $\rho$, it's easy to show that
$s \over h$$=$$\rho_{pumice}\over \rho_{water}$.
In order to prevent sinking when having a load of 1000 N, you need to have that the additional sinking due to the load shall be less than $h-s$. Or, you need to displace enough water to compensate for the added weight.
In other words,
$(\rho_{water} - \rho_{pumice})\cdot a \cdot c \cdot (h-s)=$
$(\rho_{water} - \rho_{pumice})\cdot a \cdot c \cdot h(1-$$\rho_{pumice}\over \rho_{water}$$)=100$
Therefore, if you set two among a, c or h, you can determine the other using the above formula.
The tipping moment for a slab can be also calculated and give you other constrains on the dimensions. However, a slab is not the best shape if you want to stay practical: if it is not large enough, it will tip as soon as you approach its edges (try standing on a paddleboard and you will see what happens if you move toward the edges along the shorter dimension).
To improve tipping stability while keeping the dimension reasonable, it would be better to adopt a catamaran-like hull cross section (image adapted from here)

And, since pumice over the years tend to soak in water and then sink, flame the outer surface so that it turns to glassy enamel and is better sealed against water.