Hi there. Glad to hear you have FSL.
Hypos after meals may happen for a few reasons so here goes (forgive me if you have thought of all of these already):
1 Incorrect bolus to carb ratio (have you recently become more insulin sensitive e.g. lost weight, gone to the gym more and built extra muscles) or recovered from an infection, become less stressed? If female do you get a week o f insulin resistance before your cycle starts?
2 (more likely) Injecting to early before a meal. We are all different so the standard 20 minutes may not work for you right now.
3 (related to 2) Not taking into account different rates of absorption from what your carb is being eaten with otherwise known as The Pizza Phenomenom (fat really slows things down so take a split bolus dose
4 Doing exercise earlier in the day can result in a drop a few hours later so that is worth considering too.
It sounds as if at night time you are eating something which is getting absorbed slowly during the night or possibly if the spike is towards dawn then that 's a thing too (natural physiological response to the overnight fast is for your liver to release glucose into your blood).
Its a pain but type 1 is so complicated and much more than a set of carb to bolus ratios and fixed basal doses!