We have the same floor in all our rooms apart from the bathroom and kitchen. We love it. After some months you might appreciate the dullness. Shiny floors show up dirt and dust.
I haven't come across one good peat free compost. Went to a RHS talk last night. Lots of question about the quality of peat free compost (some are just like wood chip). The advice was to feed the plants earlier.
Don't give up hope.
Manure rots down fairly quickly. In about 6 months time you will have to top it up. Fairly fresh manure might be too rich/strong for the plants and burn them.
Just took the side wall off our built in wardrobe. It was next to an uninsulated cavity wall. Clothes started to have a musty smell and felt clammy. The end board was coming off the wall in one area.
Surprisingly there was hardly any mould just a patch 2 by 2 cm. Most of the plaster is covered...
I don't think you need to turn the compost every week. You can still put more compostable material on top of the card board. We add to the compost all the time with layers of card in between.
You need patience with your compost heap. Of course on gardening programs they show you perfect compost done in no time.
In real life it takes about a year to get good compost.
Have you googled 'hot composting'?