I too take regular cub foods block cheese on trips.  Even in August it seems fine for at least my 7-10 day trips.  I never pre-froze my cheese, but it sounds like it could help.  I have found the real challenge to making cheese last 7-10 days in good shape is to protect it from the sun and mid-day heat.

Unfortunately, it only takes one mistake to end up with super oily crumbly cheese.  Hang your food pack in shady areas if possible and when the food pack is sitting on the bottom of the canoe durning your travel days, make sure it is buried below the surface of the pack exposed to the sun so it says cool.  

Nothing is worse that pulling out melted oily cheese that has been heated to 110 degrees from a sun exposed pocket of a food pack.

Gijikiki