I wouldn't try and professionalise 10's. I think it would over-complicate the rugby landscape. One off tournaments between 15's teams maybe, but I think 7's has won the battle of the shortened formats and it's in rugby's interests to grow it further.
I think if you were trying to start a professional sevens league it would be better to stick to the standard format of the game. But it might be better to limit each day of play to about 8 matches played over 2.5-3 hours. If you had an 8 team competition you could have 2 matches for each team every game day. You could use a league table format, with every team playing each other say 4 times in the league. That would mean 14 game days with a 15th for finals.
If you had 16 teams you could use the same format with 2 divisions of 8, which would make the cross divisional finals day more interesting.
15's should really be the only format for home and away style leagues IMO.