So I decided to do a bit of number crunching this afternoon to kill time, with some interesting results.
According to
https://clans.faforever.com/ there are 696 total clans, of these 530 have less than 4 members making them incapable of entering.
This leave 166 clans, of these I asked a few people of various timezones and skill ratings to have a look and see how many of the clan tags people recognised even one person being associated with, this turned 166 into approximately 28.
From this 28ish I then removed specialist clans, clans that focused on certain maps or game modes that would have them likely not participate in a clan tournament. From here we now have around 21.
Of these 21 clan I went through and actually check the clans against the requirements of the tournament, clans that couldn't field enough people with the minimum rating, the minimum games or overshot the maximum global rating with their most efficient combination of players. This turned 21 into 13
From here on out things get a bit more subjective. When you start subtracting clans that are highly likely to not enter because of reasons such as the clan being in an unfavourable timezone, having key members for scenarios that would allow the clan to participate be unavailable or highly like to be unavailable your grand total number of clans comes to 6.
6 is a dangerous number to be at as any less and you probably won't even have the minimum number of teams to even host a tournament.
I would strongly advise loosening your entry restrictions by:
-raising the rating cap
-lowering/removing the rating minimum
-lowering/removing the minimum games
Ask me about my amazing content production to watch while you wait in a lobby.