What times of day do they happen? Is it completely random, or is it e.g. overnight or when you've eaten and done a reasonable dose for food?
I find my insulin sensitivity changes quite drastically based on what I've done, but I'm never quite sure how much of an effect I will get - in the warmer months I'm riding at least 200km a week, but my riding can be somewhat variable from day to day and weekend to weekend due to childcare/work commitments, so I'm never quite sure how large an effect I will get.
I tend to counter this by splitting my evening bolus injection, which need to do anyway as this is my large meal of the day and I want to be vaguely stable on the way to bed. During the day I tend to take normal bolus (unless I've just exercised or will need to do so while it's still active, in which case I cut it) and work on the assumption that I may need a mid-morning/afternoon snack (takes me back to the majority of my life spent on old insulins with reasonably fixed eating times and quantities - nostalgia perhaps
)
I'm always hungry so eating uncovered snacks is no hardship, if I don't need them (for BG purposes) I will probably take a bit of extra bolus (based on response of the previous meal) so I can eat anyway
With a pump you can presumably change the delivery shape of your insulin - what do you currently use?
I do reduce basal if I've done or am doing a long ride, but I also have a gut feeling for when I need to do this which tends to work. I also split basal (MDI) to avoid running low overnight and to tune for exercise - you have even more flexibility on a pump. If your hypos are overnight I assume you've tried setting a higher target BG level for these periods?
As I'm MDI I'm afraid I don't really know much practically about pumps (and even less about the specifics of closed loop on a given model) but what is your BG setpoint during the day and night (I guess you run different ones?) Does the pump adaptively measure and change its insulin sensitivity values or is this a thing you have to do manually (or are you intervening to override whatever it has decided?)
I'm guessing there must be people on here who do know about pumps and also your specific one, certainly I see more talk about pumps and exercise settings on diabetes.org.uk forum, which might be another avenue for questions.
Sorry it's not a very useful response, but don't give up!