I've never run sub 1:50, but I ran 1:50 several times during my 20s and 30s. If I could go back in time I would put more emphasis on the extreme elements of the event. I avoided repeats over 1k because I hated them, and as far as working on speed, I pretty much stayed with 200 to 300m race pace workouts (8x200 @ rp w/ 200jog rest) or (5x300 @ rp w/ 300 jog rest).
I should've run more longer mile pace type stuff combined with 400m type training on the speed days.
I don't see how you're doing the wrong thing, except with your speed work. It seems like you it's all very short in duration. In the 800 you don't need top end speed or acceleration (60m sprints and short hills) as much as you need to be able to hold moderately high end speed for a long period of time. I don't think you're really training yourself to hold that speed long enough. The 600m repeats you're doing are ok, but they aren't getting you ready for holding onto 50-51sec 400m pace for as long as possible. You need to go through 400 in 51 and still feel fairly relaxed.
I'd suggest something like this.
Tuesday: 5x300 all under 40 sec with 4-5min rest. Or maybe 600, 400, 300, 200 with the 600 a second or two above race pace, the 400 at race pace, then the 300 and 200 under race pace......probably 5-7mins rest.
Sat: 6x1k at sub 3:00 with a couple mins rest.
Keep everything else similar. Drop most of the short hill work, unless you want to add a few on after the Sat 1k's.
You have all required speed and acceleration already. You just need to be able to hold your current 800 race pace further into the race. And maybe be more comfortable going through the first half of the race just a tick faster.
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Another thing to consider is that maybe your training is just fine. Looking back on my early days, I was holding myself back with a poor attitude. I wen into every race with the idea that I wasn't as good as the other guys. I felt like they were somehow more talented than I was. It sounds stupid, but I'm just being completely honest. I remember lining up against Olympians and thinking I was just lucky to be in the same race. I had resigned to just going through the motions instead of getting my mind to a place where I could be competitive and fully push myself. I knew how to kill it in workouts, but I was weak during the races. No one would have guessed from watching me though -- I appeared as confident as the next guy. But I was focused entirely on the wrong thing.
I'm actually much better as a masters runner. I have a healthy attitude about racing, and I'm not really worried about everyone else in the race. I just try to win. It's too bad I couldn't have that attitude years ago.
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Finally, the thing about not having time to run doubles. I'm not buying it. Get up early, then run the real workout after work. I've done it myself with a full-time job (60 hours per week), plus having a family (and I'm not a deadbeat dad....I cook dinner nightly and split pretty much everything 50-50 with my wife).
If you think adding easy mile sin the morning would help you then that's what you need to do.