An A1c of 11 equals an average blood sugar of 280, which, as you said yourself, is on the very high side. When you have consistently high blood sugars like this, you become more insulin resistant and the potency of your insulin, as it affects YOU, decreases. For example, if when you are in a normal range of say 80 to 140, one unit of insulin lowers your blood sugar by around 30 mg/dL, at 280 the same one unit of insulin might only lower your blood sugar by 20 mg/dL. This will throw all your calculations off and cause your blood sugars to be even more unsteady.
So, from your present average sugar level of 280 you have a long way to go before going low should be a serious concern. If I were you, I would set a short term intermediate blood sugar goal of 180 mg/dL,, which if you reach it (or should I say "WHEN you reach it," because I KNOW you can and will do it!), would "earn" you a greatly-improved A1c of around 8%. Wouldn't that make you happy and set you on your way? At an average blood sugar of 180 not only will you benefit by the lower risk of future complications, but moreover you will benefit in the short term by your insulin dosages becoming more potent AND predictable. Only then should you set your average blood sugar and A1c goals any lower.
That being said, I want to add perhaps something I shouldn't say, both because it might instill false security in YOU and jinx ME! Anyway..., in almost forty years with Type 1 Diabetes and quite frequent low's, I have never gone into insulin shock or passed out, never had to be take to the emergency room, never had to be assisted by an EMT, and always been able to help myself... by myself. While there have been some close calls, I have never even fallen or been injured as a result of hypoglycemia. (Knock on wood, as my Mom would always say.) So while I don't want to downplay your fears and tell you that hypoglycemia can't be dangerous, I would like to say that your fears may be greatly exaggerated.
Because your blood sugars have been running so high for so long, you should expect to feel low even when you are not, perhaps even at levels of 140. And yes, it will be uncomfortable at first. But you will get used to it, and quite frankly, you must get used to it. I suggest that you push your blood sugars to lower levels when you are home or are in familiar surroundings at first. Always have your test kit and some fast-acting sugar (eg. glucose tabs, 4 oz. juice or regular soda, etc.) on hand, preferably on you even at home. Make sure your family and friends know that you are striving for lower blood sugar levels and discuss with them what you'd like them to do if you go low and can't help yourself. (But, like I said, this hasn't happened to me in 40 years!) Finally, monitor and keep a written log of your progress. Feel free to post your results on line in the "Daily Diet Exercise and Blood Sugar Log" thread. All we want to achieve at the start is a daily blood sugar average of 180 mg/Dl, perhaps trying to stay in the range of 140-210. Let's eliminate the 300's, 400's and even the over 250's at first. I know you can do it, and we're all here to help.