LM wrote:No. 56 speed will cut it with very good endurance.
Honestly though, the basic speed seems to be close to there. 13.16 is enough speed to run mid 57s 400. If that gets down into the high 12s range then you should have the potential to run that
I have never in my life seen a runner break 2 without being able to run at least 54-low open. I've seen plenty of 54 high/4:20 guys stuck in the rut of 2:00 - 2:03, but to get past that hump, it just takes more speed, pretty much regardless of how good one's endurance is--even more so at a high school level, where endurance usually isn't very far developed. Having a stronger 5k PR isn't helping you when your entire body's locking up the last 200 because the first 400 was too close to your top speed.
To get dragged to a 1:59.9 in a good race, you'll really need to be capable of 53 mid (you might get away with it if you can do 54 and 4:20, but 53 / 4:45 is often a more realistic way to approach it). To really break into the sub-2 range consistently, you'll need to be able to run under 52.5.
With that being said, young 800 runners will see the biggest improvements by training to their strengths, not their weaknesses. I hate to say it, since you seem to think of yourself as a speedier type, but your PRs don't say 400/800. Hell, they say 1500/3k more than 8/15. Either way, you're not going to approach sub 2 from such a sprint-oriented base--especially not until you have much, much better overall fitness. The workouts that I'd say indicate sub 2 capacity would require you to be doing repeats significantly faster than you can do open 200s, 400s, or 600s.
So it's time for you to be building a foundation. Put in a lot of miles--from the look of your training, probably haven't been doing more than 20 - 25 MPW consistently, and you don't have the speed or fitness to get away with that. Sprinters moving up to 800m can sometimes do that. You're a mid-d runner who's moving down. Run more. Worry less about auxiliary stuff--core is great and all, but running should be your priority. You're in base phase; put in miles and fitness will improve.
You're doing way too many workouts way too early in the season. If you want to be peaking for, let's say, 2:10 in may, you don't want to be burning yourself out with a ton of workouts now (and you're running...literally a workout every day). Do some strides (at the end of long runs), hills, and if you're really eager, some 200s once every other week. Put in a longer workout each week.
Also, with all this being said, I still believe that you'll find your stronger events to be 15/3k. There's one big variable we've been neglecting here, however: you're what, 15? 16? If you're lucky, you'll grow a lot in the next few years, so just keep training, put in the miles, and see where it takes you. Don't worry so much about specific workouts--your fitness level isn't there yet. Put in miles, put in base workouts, and do some occasional strides/200s to stay in contact with your speed. Your weeks shouldn't be looking like the one in the OP until you're in the heart of competition phase.