The easiest solution would to be give teams first slots then award remaining slots to the provinces to hand out, similar to how Worlds are handled. Determine how many slots the match can hold at a given venue and then distribute them.
Remember, this is our National Championship. It is run in the same basic format every year. Primarily you have to shoot over two half days. That's part of the contest, to see who can come out and perform their best in that situation. It's a bit different from having a good or a bad day. You have to be prepared to shoot your best on multiple days. Personally I'd like to see it shot over three or four half days. In Ontario we are too used to one day matches where you shoot and leave. It's a different game when you go somewhere else and have to shoot multiple days like a European match, US Nationals, area matches or Worlds.
As for having a longer match, it would be nice but as mekanik pointed out, not so simple. Staff already has to be there for a full week as it sits now, which is one week off work for these people too, to run longer you are looking at the whole staff having to take almost another full week off work and since the match covers those officials rooms etc that's gonna be a hefty bump in the match fee too. These people already give up a week of their work and vacation to put in this match for the shooters, asking to give up another full week is a lot to ask.
Add to that most ranges are hard pressed to be closed to their members for a week, let alone two weeks. Last year the schedule was, set up sun, mon, preshoot Tuesday, match proper wed-sat, tear down sun, turn range back over to club Monday. That's all the time you have and even at that it's tight with the set up.
The reality is this format works really good. As HB said, it's a good sign for IPSC in Canada that that many people want to shoot Nationals, but not everybody can. We have to figure out how to make the best of what we have so it's fair for all the provinces.
I know the guys in NS are working very hard at making this an excellent match. Please send them your thanks for taking this on!