It is really hard to exercise AND lose weight when you are Type 1 without running into Hypoland or Hyperland. If you were on a pump, I would say to reduce your basal too. But if you are not, and you want to run without stuffing your face with carbs (which is how it always feels to me), I think your only option may be to change the timing of your run. That's difficult if you have a full schedule, or a working life. Some people do it by running early in the morning. Alternatively you could try running before dinner, instead of after. The idea is to run when you haven't got BOB (bolus on board). Bob's a generous type - always makes people eat and so makes them fatten up in spite of exercising.
One thing that does happen in your favor, though, is that as your body gets used to a particular type of exercise, it doesn't burn off quite so much glucose. So even what you are doing now, though you don't like the walking part, is helping you to get there. Hopefully then you can start at a lower level without such a fall to follow.
Quite soon, you should see effects on your insulin resistance so that you basal requirements should drop, as well as your insulin:carb ratios. As you build muscle your insulin requirements do go down. You may also see drops overnight.
Diabetic Athlete's Handbook by Sheri Colberg is good on all the things to do and expect when exercising. She also recommends a 4-6 week run-up to a full-on training plan to get over these "bumps".
It might take you longer than 9 weeks or so, but you can still get there in the end.
Another thing is to eat "slow release" carbs with fat, like peanut butter on toast, before you run, but a) I don't know much about that, and b) it's quite a lot of calories, so if you want to lose weight, I suppose you'd have to cut those calories from some other point in your day.
