Hi Lucy!
I have LADA which is a slow-onset form of Type 1. I take Levemir basal split morning and evening and Apidra rapid-acting with meals. I find that if I eat a carb-rich meal, my BGs are uncontrolable now matter how carefully I count the carbs and work out the insulin doses. The way I control my BG is to keep the carbs very low and certainly cut out or reduce to tiny portions all the major starch carbs - bread, pasta, rice, potato, cereal. Would it help if I give you an idea of a day's meals for me?
Breakfast - 50g raspberries, 75g full-fat natural yoghurt, 15g granola - 2.5 units Apidra to cover
Lunch - whole chicken breast, salad leaves, cucumber, 2 or 3 cherry tomatoes, red pepper, radishes. Half a small orange (about 50g), a tablespoon double cream. 1.5 units Apidra to cover.
Tea - home-made chilli. Sugar-free jelly, cream. 3 units Apidra to cover.
If I need to snack during the day, I'll eat a piece of cheese or a handful of mixed nuts.
Obviously if you cut back on the carbs you will need to reduce your bolus doses, so do it carefully and slowly.
The other thing the struck me with your description of what is happening is that maybe your basal dose is wrong. Your basal dose should hold you BG steady through the night. If your dose is correct, you shouldn't rise or fall more than about 1 mmol. The way you can test this is to fast from early evening so that you don't eat or take any bolus after say 5.00pm, but jab your basal as usual. Test before bed then set your alarm and wake and test every couple of hours through the night. If your BG rises your basal dose needs increasing, if it falls your basal needs reducing. It is almost impossible to get your bolus right until you have got your basal right, so that's where i would start.
Good luck
Smidge