Will these K-alum crystals combine into a "cohesive/well-glued" mass?
According to the Wikipedia article Potassium alum, the dodecahydrate melts at 92 to 95 °C. So if I wanted a large lump, I'd put the salt in a test tube (or some other container), dunk the container in boiling water to melt the salt, then pour the melted salt into some type of a mold to cool and solidify.