I always try to keep the things simple So here is the simplest solution for doing this

as you have already reached a stage where you just want to fill the white GAP so that, they merge together without a seam, You can use patch tool for it.

make a selection with Rectangle marquee tool around the Gap then select the patch tool and drag it to its side portion. Photoshop will atomically calculate the pixel interpolation and gives you a much finer result that any other method can't. Here is the Example

I always try to keep the things simple So here is the simplest solution for doing this

as you have already reached a stage where you just want to fill the white GAP so that, they merge together without a seam, You can use patch tool for it.

make a selection with Rectangle marquee tool around the Gap then select the patch tool and drag it to its side portion. Photoshop will atomically calculate the pixel interpolation and gives you a much finer result that any other method can't. Here is the Example