The entire process is incredibly technical and still not completely proven so you'll likely get answers that are a combination of fact and opinion.
As mentioned, with type 1 more than just our beta cells are affected by the disease. Personally, I believe that the answer lies in our pancreas' alpha cells and particularly how we regulate our glucagon hormone.
It seems glucagon management is affected in very different ways between people with type 1 and type 2. In people with type 2, there seems to be an issue with glucagon management in normal or hyperglycemic situations, but not in situations of hypoglycemia. That's why some people with type 2 may have issues with fasting glucose levels, but rarely does a type 2 have issues with hypoglycemia (ignoring medications that cause it).
In people with type 1, the insulin:glucagon relationship is obviously affected as we lose our natural insulin production. The issue seems to be that our alpha cells don't react to artificial insulin like they should.
My particular theory revolves around excess protein consumption and gluconeogenesis. Several studies have been performed to show that excess protein did not result in hyperglycemia for MOST people with type 2, but that was not true in people with type 1.
Furthermore, there was evidence in these studies to show that excess protein DID have a positive effect at correcting hypoglycemia in people with type 2.
How I've implemented this into my own approach:
I consume a significant amount of protein each day (often more than 1g/1lbs of body weight). That's for several reasons including: I'm interested in bodybuilding, I love eating meat, I have perfectly healthy kidneys, and it seems to have a positive effect at avoiding hypos for me (although that is a theory not a fact).
Similar to a basal/bolus insulin management, I believe there may be a similar relationship in a basal/bolus GLUCOSE management theory.
The excess protein I eat is my "basal glucose." It WILL raise my levels, but generally at a much slower rate (possibly over a 24hr period). While this creates potential issues with waking hyperglycemia (think dawn phenomenon), it's much better than having the opposite problem while I sleep. Only time will tell if this will continue to be an effective approach for me. Note: I AM able to gain weight (and quite easily) with this approach.
Obviously, my "Bolus" glucose would be sourced from carbohydrates. However, I regulate that by eating fewer than 50g of carbs each day (Bernstein's law of small numbers).
The end result is significantly reduced blood glucose volatility. Instead of having to worry about very rapid onset drops or spikes, I have to worry about drops or spikes that usually take longer than an hour before they become potentially serious.
Again, time will tell if this approach will continue to work.