Hi Leslie, I am also very insulin-resistant so I understand where you are coming from! I second Helen's comment that it isn't a competition. Some people are insulin-sensitive, some people are insulin-resistant. It's just the luck of the draw. And by the way, don't beat yourself up about your weight. You can be thin and insulin-resistant, and you can be fat and insulin-sensitive.
If you need the insulin, you need the insulin. Needing more insulin doesn't make you a bad person or a hopeless case. You need what you need to keep your numbers under control.
Having said that though, there are a few things you can do to try to tackle this. The most urgent task as I see it, is to get your blood sugar down to more normal levels. The higher your blood sugar, the more insulin-resistant we tend to be - so that's not very helpful when one is insulin-resistant to start with. I myself find that once my blood sugar is high (which for me is anything higher than 160 or so), it is stubborn and sticky, and takes a LOT more insulin to lower by one unit than it would if my blood sugar was in range.
The other thing you can do is to really cut out the carbs, at least until you get your blood sugar into a normal range. 60 units of Novolog at a 1:2 ratio means you are eating 30g of carb per meal? That is not high carb by the standards of the 'normal' world but diabetes works by somewhat different rules. Could you possibly bear to go lower carb than this? Or even zero carb? Again, this isn't for forever, but just to get your blood sugar into normal range.
Finally - and some might disagree with me here - one suggestion is that you could try changing your basal insulin? Levemir does not work very well for some people. I'm one of those people. For more than a year from diagnosis, Lantus gave me pretty good morning numbers. But then I got switched to Levemir and despite taking double the dose, I woke up high every morning. Waking up high is such an awful start to the day and pretty much ruins my mornings. I lasted two weeks on Levemir then rebelled and put myself back on Lantus.