How is this idea for cross country training?

I’m a cross country runner, and this is an idea I have for training, tell me what you think of it. Ok, well to start off the focus of my training is to improve my muscular, not cardiovascular, endurance. I have absolutely fantastic cardiovascular endurance, and the only thing preventing me from running faster times is that my muscles just get wasted after a while and I can’t keep the pace of my first half. Again, its not cardiovascular, as I can hold my breath, have a conversation, all of it and during a race. And still get great times. So, to improve my musuclar endurance, my idea is to , staring today, do stairs at absolute max, 5, up and down, at a time (its about a hundred steps up). Then do Stassi Squats, and repeat until I am absolutely beyond exhausted. I feel that if I can continue this for a few weeks, perhaps my muscles will be able to keep up with cardiovascular endurance, and I’ll be able to run much faster. Any comments, advice, and the like would be appreciated.
First person says that’ll build cardiovascular, which is true, but won’t going up stairs also build muscular endurance? What can I do to as quickly as possible strengthen that?