There are some pretty big sites hosted on non dedicated servers, by the sounds of it, it's just the particular server you're on and sharing that is probably being pounded by something else during the day or has technical glitches.
Rather than looking for an expensive dedicated server you might want to go the middle ground and *not* look at the super cheap hosts but instead try to find a more local Vancouver host that is maybe a bit pricier but has more personalized service and may even throw in a deal for a small credit on the front page "host provided in part by blah blah blah" (which is something a local Vancouver host might be very interested in considering the geography of the visitors for this particular site if you can show them the number of visitors you get historically).
Godaddy and the big hosts are cheap but you are nothing more to them than one of millions of customers and the actual server could be anywhere in North America, being on a local Vancouver host gives the visitors a faster connection (less network hops) and you will get more personal and responsive service.
There are dozens if not hundreds of local hosts, I would shop around and see what kind of a deal you can get for partial sponsorship. I can't see a sales guy not liking the idea and giving you *some* kind of break on the costs, plus if their name is on it then it's even more incentive for them to keep you up and running.