A lot of people (me included) find that they are a lot more insulin resistance when their blood sugar is high, so I can see one reason why you are having issues if you are always starting at a point where your blood sugar is high.
I also find my insulin needs go up when I gain weight. In general, I do need more insulin than I did 40 years ago but I just take however much I need to balance my blood sugars. I (unfortunately) find it a lot easier to gain than lose weight, but I have found some success when I reduce the carbs in my diet and watch the cheese and alcohol. I also find that I tend to gain weight when my blood sugar is high. ( I stress that this is just my personal experience.)
There are U200 U300 and U500 insulins for insulin resistant folk who need large doses, though I'm not sure which brands have the stronger variants.
Good luck. I have to say that I feel your team have left you in the dark by never educating you about carbs though. It's very easy for them to assume that long term T1s know everything and don't need further education, whereas this can be far from the case (for me anyway). Luckily when I was a child and on fixed doses I was also on fixed carbs so learnt to cab count then, though i's only relatively recently that I've properly understood how a basal/bolus regime works.