First off, don't give up. Your first time progressing from Normal to Hard is going to involve just as much growth as your first time playing Touhou. When I was at that stage, I was still learning new mental and physical tricks to improve my playing ability. And although you may think you know how to devise new strategies based on each new detail/mechanic you learn about a spell card, this was an area that I felt got much deeper than I initially predicted.
I can only speak for myself, but I've literally never been happy with my 'current' 1cc before attempting to learn the next difficulty level. Like you, I would want to become more skillful at normal 1ccs (especially more consistent at the stuff I know I can do) before I would want to attempt hard (1cc or no), but that's not the way it ever ends up. I mean, there is a benefit from playing normal some more after your first 1cc, but after ten 1ccs there won't be as much. I recommend playing both Hard and Extra before you think you are ready for them. That's always how I feel when I do them, and its always what gets me to improve from normal.
Extra especially shouldn't be overlooked. I think the focus on cards and not stages is better for improving the fundamentals, and Extra cards are better than regular cards for this too (at least I think so).
There are several reasons why you might be able to clear cards during practice but not during live runs. You definitely aren't alone here. The solution though is to do stage practice. It could be you need to practice the live concentration and/or getting used to being in a poor situation at the start of the card. It could be that you need to practice "cold" clears, where you don't have chance to warm up against the card. There's also the reality that unless you clear rates are 95-99%, then an entire stage is often going to have misses. Using stage practice you can figure out which cards are worth bombing with very liberal bombing discipline.
