I have been cleaning my parquet floors (well, the ones which I haven't carpeted over because I got so fed up with cleaning 'em) using natural wax. It is the only product that works. It does bring the floor up beautifully.. I know what you mean about water marks though. You have to dry them up immediately. At least this polish is non-slip which is important. wax
I used to have a lot of parquet flooring at a previous house, and used something from Lakeland to clean, and then about once a year something to seal it and keep it very shiny, it looked wonderful.Sorry I cannot recall the names of the products, but have a look at their website if you can’t get into their shops.
Our whole bungalow has these and I have tried all the things that are recommended for it. The problem is that the GC hurtle about and leave drops of water and scuffs in their wake.