We found 3 Reddit comments about Amrex Sponge Electrode - 2"x2". Here are the top ones, ranked by their Reddit score.
Don't use those sponge electrodes - they're too small. The reason people are adapting the foc.us device in the first place is to reduce the current density (i.e. Amperage per unit area). The reason this is necessary is, H2O + NaCl solution, under high current density may behave like NaOH (lye) and HCl (hydrochloric acid). To enter a lower energy state, the OH- and H+ ions may bond to skin, rather than one another, causing chemical burns.
The solution is to reduce the current density, either by lowering the current, or by increasing the size of the electrode. It also helps to use lower salinity (0.07-0.15 Mol seems to be best - that's roughly 1-2 teaspoons per liter) to wet your sponge electrodes.
Typically, scientific studies use sponge electrodes that are about 25-35 square cm (i.e. ~2x2-2x3 inches), like these Amrex electrodes. Problem is, there are very few online suppliers, so they're selling out of them quickly.
My solution has been, cutting up cellulose sponges and using alligator clips to connect them to my tDCS kit (The Brain Stimulator). That may not be an option, since you have the foc.us device, but you may be able to do something similar by taking a cellulose sponge at least 2 inches x 2 inches (5 cm x 5 cm), and placing it underneath the built-in electrodes.
Eh, did I mention they are 2mm? Whoops. Besides replacement leads from places like Amazon I haven't seen any. My original set fell apart and I ended up re-soldering them on thicker gauge with sugru insulation. Never bought others and definitely not in bulk.
Amrex sponge electrodes take banana plugs as do many carbon electrodes. In fact there's a recent link on here that has all of the above, if not quite in the Mouser quantities you might want.
I'll add it here.
They must be available elsewhere but I've just been using Amrex like these from Amazon for a while now.
seriously, there is a significant structural difference between yours and proper sponges, that's probably where your problems are coming from.