This is a well thought out and detailed post, thanks. I wish all questions were like this.
Sounds like you are off to a great start, that's good. One thing I'd like to clarify - you went from couch to 63 miles in 3 weeks?? Or did you mean 3 months? I'm going to assume you meant months for the rest of this answer because that would be insane. But just in case, make sure to take things slowly in terms of increasing mileage - no more than 10% per week of volume increase.
You're right that speed-work isn't necessary to improve for most people, increasing mileage is. However if you're already running 63 miles per week, I think it's time. Here are some recommendations.
The first thing is the long run, which you touched on briefly. I am a big believer in the long run. Don't increase your weekly mileage, but instead move some miles onto one longer effort once a week, maybe 20-30% of your weekly mileage. The other days should be shorter so you can recover more
Second thing is the tempo run, which is a "comfortably hard" pace, or in other words the hardest you can hold for an hour or so. Usually done with warm up and cool down.
Third thing is intervals/speed-work. There are many schools of thought on this from many authors focused on many races, but I've found success with the following: 12x400 meters with 2 minutes rest, 6x1000 meters with 2-3 minutes rest, and 4x1 mile with 3-4 minutes rest. The rest can be standing, walking, or jogging, depending on where you're at. The intervals are done at or near 5k pace. NOTE: CURRENT 5k pace, NOT goal 5k pace.
So instead of running 9 easy miles every day, your week might look like this.
Monday: 6-8 miles easy
Tuesday: Intervals (example: 1 mile warmup, 6x1,000m at 5k pace, 1 mile cooldown) 5-6 miles total.
Wednesday: 6-8 easy
Thursday: 1 mile warmup, 40-60 minutes at tempo pace, 1 mile cooldown. 6-8 miles total.
Friday: 6-8 easy
Saturday: 10-15 miles long run, easy pace
Sunday: Rest/recovery run
Some people like to do a mid-week medium long run as well (i.e. 10 miles on wednesday instead of 6-8).
Using this method of base building I was able to go from 27:00 to 18:45 in the 5k in about 9 months. Now I am starting an authored training plan.
When you get used to long runs and speedwork, I encourage you to read Faster Road racing my Pete Pfitzinger or Daniel's Running Formula by Jack Daniels, and following one of their plans. I am doing the Pfitziner 55 mile per week half marathon plan right now.
Additionally, come on over to /r/advancedrunning for some discussion on the more serious/competitive side of running. :)