It is BBA, not diatoms. Very common when plant growth is exceeded by light available and the curse of low tech set ups. As said, cut the lighting timings down slightly and feeding micro fertilisers (the basic weekly stuff is all you need, none of the fancy high tech things). I suspect that a lot of the micro nutrients that come with the substrate etc have eventually been exhausted by the plants, which have slowed their growth, which is why we tend to recommend at least the trace fertilisers on an ongoing basis for planted tanks, but otherwise you're spot on with mechanical removal, although it sometimes needs a bit of elbow grease to get rid of. On things like rocks you can use a little bit of plain (no added extras) thin bleach and then treat the rock with dechlorinator afterwards, which can remove it, otherwise peroxide or an overdose of liquid CO2 works. All out of the tank of course.