I do think some of this will come in time as you gain strength, conditioning and confidence. I would also suggest adding some cadence drills into your interval routine. Having ridden with you, you do have a nice spin, even without the benefit of clipless pedals (although I think they, too, will ultimately help). My guess, however, is that you could spin a bit faster with some practice. That will help you build better aerobic capacity, too, which is a necessary building block for speed work.

All that said, I would strongly encourage you to just ride. In my experience, there's only so much you can work on at one time. Between bike handling, endurance and distance,you already have a lot to focus on. I know you already know this, but try to remember and accept that it will take take more than one season to meet all of your goals. So, be patient, grasshopper!