Thanks for sharing, I try to address a few things.
Rest periods: if i do a subthreshold run, does not need to be EIM, i avoid now walking, because as you said the brain gets used to it and this is a problem. So e.g. the 1000m EIM i do not walk.
However i walk shortly after the 200s and also 400s, so above threshold. Especially after the 200s at vVo2max.
Running hard: You can do so of course, that is also written in the book. The EIM assumes that you race regulary and there are substitute race suggestions included in the book.
Lonely: i personally do not follow the EIM 100%, now after more experience. I have included the idea i would say, but not all. Eg. i do the long run 21km, and have EIM included. But i have also a trail unit every week with friends, and sure as hell i will not exchange that. So no need to do all units that way.
Missing something: I had the same feeling. So i have done a threshold run, a tempo run, a sub-threshold run, and so on. I guess that method is good enough to stand alone as single units and can be integrated as needed.
Monotony: A very important point. I read in a book that you should change your training methods every 6 weeks, to get new stimuli, because after 4-6 weeks the body stagnates. So i mix it up and i guess this is a good method to do so.
So my tip is to open up your training units.
I have the same goal as you 5k in 20minutes and same as you i failed :) So we can shake hands here.
I am quite heavy (for a runner) with 83kg 183cm height, and i calculated 4kg less would do the trick. But i let the weight drop by dong the training. If i do age and weight grade i am quite in a good shape, so overall i am very happy.
At the moment i play around with 2, 3 minute intervals subthreshold (only 1 minute to 90sec rest), because Kipchoge and Norwege athletes does that too. Kipchoge does no tempo runs, that is very interesting.