I really don't think it's a problem with their processor. If they are actually working with a third-party processor like Cryptopay for all crypto transactions, then they could have just initiated the order with the processor immediately when they deducted the amount from your balance. The conversion at Cryptopay should be near-instant and certainly wouldn't take days.
One thing I just looked up: it seems Cryptopay doesn't support CAD, only USD/GBP/EUR. So your situation is even more similar to mine than I thought. At the end of the day they can argue that it was expensive for them to convert your CAD to USD/GBP/EUR and then more was lost in the conversion to LTC. They will offer no transparency on these alleged conversions.
Based on my experience with them, there are some really awful human beings working there---like scum of the earth types---pretty high up in the chain. The only thing that can make such awful people change their ways is the threat of losing money/reputation, so you're doing the right thing by posting here.