Insulin does work far more effectively you suggest
Just read the Banting Nobel lecture From the first they demonstrated that insulin saved lives inboth children and adults. Diet is mentioned as OK for 'mild' diabetes in the over 50s, otherwise the pronosis for everyone was poor. Luckily we've come a long way since then and for those that diet doesn't work and who have some insulin production there are other medicines. Some people may need one type, some more than one type and some may require insulin . If diet doesn't work because there is too much resistance or too little insulin surely it makes sense to give these medicines a chance.
http://nobelprize.org/nobel_prizes/medicine/laureates/1923/banting-lecture.htmls e
When I was diagnosed like lilibet I was hospitalised, my fasting BG was 21mmol, I was very ill and losing weight.
Insulin brought down those high levels within 3 days.
My first logbook (10 days after that fasting test) shows a highest post prandial reading of 10mmol, my average fasting glucose for that first week at home was 6.5, six months later the first page of the next log book shows an average fasting of 5.3mmol and a highest reading of 7mmol. My highest Hb A1c in the four years since then has been 5.6%.
Without insulin I would probably not be writing this, I wouldn't be alive. Incidenlty, I do not restrict my diet in 'extreme ways', though I probably exercise more than most.
Your readings are erratic, but I feel (from a lay point of view ) they point to an insufficiency of insulin but you may also have some resistance : the higher levels you have, the more resistant you are likey to be. You go to bed with a high reading and wake up with the same one, you are therefore able to tick over producing just enough insulin for your glucose needs during the night but not enough to reduce the high level. That high level i will be causing damage to other systems. Hb A1c is highly correlated to many peoples' overnight blood glucose levels, after all it accounts for up to half of the time.
You are obviously not producing enough insulin to cope with the carbs in your meal, though your production or insulin sensitivity may vary from day to day. It also seems that when you exercisie and your muscles need some more glucose, the liver is producing it but there isn't enough insulin available to utilise it. As people have already pointed out, you may have LADA.
I think you have said that you are losing weight, remember that it is not just fat that you are losing, it is muscle and the heart is a muscle.
Thank goodness we have medication, without it many of us would have died of starvation or quickly developed life threatening complications. Please, do not adopt an approach of doing nothing. If necessary look upon it as an experiment but go and discuss the alternative medicines with your doctor though realising that it may in the end be advisable to accept his suggestion of insulin.