Agree with Sam. On that much Insulin you will swing. I found changing to Low carb enabled me to have tiny increments of insulin, to be honest my problem is the opposite of yours I am insulin sensitive. The small amounts of insulin ,instead of larger doses to deal with the Carbs, made things so much more controllable for me...no roller coasting blood sugars.
Some people can manage carbs on insulin, some can't, there is no hard and fast rule for us all. You just have to realise when things are not working and try a change of tack.
Hypo's can happen for all sorts of reasons not just getting doses wrong, Cortisol problems, Hyper Thyroid, all sorts of underlying conditions can cause them. Coeliac also. I'm not saying this is the case for you . Give low carb a try for a month or two and see if things improve for you ,if not, then you can go back to the starchy carbs and look again.
Hypers, not enough insulin. High Cortisol levels and Low Testosterone can cause Hyperglycemia in Men as underlying causes, even with little carb intake, again probably not you but it is worth getting your Endo to rule out underlying causes. Testosterone promotes insulin sensitivity in Men, but has the opposite effect in women.
I would certainly start with diet changes first and then take it from there....Good luck with your HCP app!
Read the low carb section on here, and holler if you need any help