Export your model from Blender (or any modeller) as OBJ, FBX or glTF with UVs. STL has no UV data, so it can't be painted.
One mesh at a time. The five maps are one texture set for one UV layout, so loading another mesh replaces what you've painted. If your model is several parts, unwrap them together onto one UV layout.
Import a mesh, and this reads its real UV layout straight out of the file so you can paint directly on it: the same idea as Shirt Maker and Pants Maker, except the template comes from your model instead of a fixed Roblox one. Paint all five maps a SurfaceAppearance accepts, judge them against a live lit preview, and export PNGs named for the exact property each one belongs in. Your mesh is read in the browser and never uploaded anywhere.