I guess the percentage of soil organic matters(SOM) isn't too high. Usually 5% is considered good for
gardening, which can be achieved easier in the small scale by bringing in outside organic matters as you've done.
For a large scale, if the initial OM level is too low, it can take a very long time to build up naturally. USDA said soil OM can gain 0.1% a year with good practice. My backyard has a SOM of 2% for many decades with no improvement at all. I doubt mowing high and less frequently is enough to change anything. In the book "Cows save the planet" about holistic livestock management, the author mentioned that in the case of deteriorated soil, some forms of soil disturbance to add organic matters to the soil are necessary. Digging zai pit and put down cow dung is an example, properly managing livestock is another one.
If bringing in cattles isn't possible, maybe you can broadcast mixture of seeds to increase the biodiversity and that will help in the long term.