Are you in frequent touch with your diabetic team? I agree with the others that you may have too much insulin in your system to cope with your active daytime activities, you should be able to sort your insulin so that you don't need to snack all the time to keep your bgs up.
Maybe consider trialling a freestyle libre cgm from Abbott so that you can see what your night time levels are doing? (If you're in the UK they should give you a free trial of one 2 week sensor) . It's possible that you are running low all night and only going up in the morning because your liver pumps out sugar then (dawn phenomena).
Do you go hypo during the day when you're not so active? Long term, there are 12 hour basals that your team could put you on if your basal needs vary day and night, so you could inject less basal when your insulin needs are less, but that's up to your diabetic team. (Though don't hesitate to tell them about your hypo issues, as you really shouldn't be going hypo all the time.) Very long term, some people use insulin pumps if the need to vary their basal, but I get the impression that you have to be diabetic for longer before they'll consider that.
Good luck.