Your 10 team round robin works just great - I am scheduling a curling event for 9 teams on 4 sheets of ice and it will work.
It is balanced with everyone playing 2 rounds on each of 2 sheets (courts).
Is there any way to avoid teams from having to play two rounds in a row on the same sheet (court) which in the case of the draw
that I see, is on the fourth sheet (court).