I'd be careful not adding too much sucrose. You can get off flavors, specifically apple.
Have you ever got this and been able to trace it back to sucrose? This is an old wives tale, that came about when kits contained a lot of simple sugars, yeasts were poor, and fermentation practices left a lot to be desired (like "just pour the dregs of a couple of bottles of XXXXXXX in for the yeast").
I'll second that. I like demerara and jaggery for this sort of thing. Overall, I added 5 pounds of sugar, about 4 oz every other day for a while and it came out great.
Demerara is pretty much the same thing as plain table sugar. It is just not refined as much. In essence, demerara is white sugar with some impurities left in.
A good rule of thumb is simple sugars should not make up more then 20% of your fermentable sugars.
Probably 10% is more like it for most beers to ensure you get the malt profile and do not thin the beer too much. Belgians can be up to 30% and more. It all depends on the beer.
This particular beer, takes upwards of 50% simple sugar. If treated right, sugar will not produce off flavors, and can be part of the signature of a great beer.
To answer the OPs original question. Once the original yeast has finished fermenting the beer to dryness, which is a finish below 1.010, you would then add the champagne yeast with the first simple sugar addition. As noted previously by someone, the champagne yeast will not convert the complex malt sugars, so the fermentation of the malt needs to be done before the champagne yeast is added. Champagne yeast is also a killer yeast, so once added, the original sacc yeast will quit working.
Beware though. If you continue adding sugar and monitoring gravity, once you get a finish above 1.010, the champagne yeast is also done. At this point the beer will not carbonate in the bottle. You will need to keg to get it carbed. If you bottle, you might want to plan the abv to about 14% and bottle then to ensure it will carb.