I have a similar, though a bit simpler situation: I don't remember the dates of one of my trips, only the month, and I can't check my (expired) passport since my country used to take them away after issuing a new one.
I remember there was a specific line in the CIC instructions: If you can't remember the dates of yout trips, enter approximate dates.
That's what I did, and I've also added a line about this in my LoE. I'm not sure about what to do if you don't remember the trips themselves. Maybe try to do some detective work, look through the dates on your photos, etc?
I think it's better to enter everything to the best of your ability and then explain it in the LoE, as StAnger and MooseNBooze said.