I suggest using individual images in Tiled and then pack your images into an atlas for use at runtime (see AtlasTmxMapLoader). This allows you to change how the images are packed (padding, which images are on what atlas page, etc) without breaking your Tiled map.
Not using Tiled as I need way too many features and customization that would be very hard with tmx and the editor / that the editor doesnt have anyway.
So I wrote my own tile system and especially very elaborate editor.
Even if I would be using Tiled: separate images for tiles... thats a nightmare for the artists. Every time there is something bigger than the tilesize they would have to cut it up, and then you would have to somehow pack it perfectly onto the tileset which happens automatically.
Otherwise you could maybe fork libgdx, see the Mesh constructor which takes a VertexDataType. You'd need to add a new VertexData implementation.
Thats for the pointer.
trollwarrior1's approach is even simpler, just move UVs one texel toward the region center. This will stretch your images but filtering won't pick up neighboring regions (it will pick the texel you excluded).
Gotta try it out, but I would imagine it looks like crap :o