Don't go away from this thread. As you said, you've had replies that have hopefully helped you. I've asked lots of questions on this forum, and sometimes very similar questions asked in a slightly different way, and there are always people who are happy to answer.
There is a point at which running fitness does translate to cycling, but it doesn't involve pushing big gears. You've got a good level of cardio fitness through running, and that will make you very capable of spinning (turning the pedals fast) in small gears, which doesn't work the muscles so hard, but does give your CV system a good workout. So, I think small gears is the way to go if you want to make quick progress with cycling, and you can always practice climbing in bigger gears later on, as you gain confidence and develop your cycling fitness.
Whether that means changing your bike or not is another matter. You can change all the components on any bike, but there comes a point when it's cheaper to replace the whole bike.