I actually quite like this thread. It makes you think.
Oscar you actually remind me of myself in this thread lol. Although I'm not sure I should admit that
When I first started training, I had this old BB and DB set, which came with a big poster with pictures of all the exercises you could do with said BB's and DB's. Some how, I didn't take this as all the things you CAN do, I took it as all the things you MUST do. So, my program took me about 2 and a half hours, it covered everything in detail apart from maybe my toes, and it crippled me for about 2 weeks every time I tried it. I could barely walk and couldn't even straighten my arms, never mind lift them over my head. Needless to say I didn't stick to it. Although I did learn a valuable lesson - More isn't always better. Although sometimes it is. Oh, and not to take things too literally.
Anyway, i'm also a little lost when looking for what you want from this thread. One thing that jumped out at me was your goals. They're great. However, they're general, non specific goals. I think you would benefit in drilling down some more specific goals, and creating your program around this.
You say "over all strength". I say - Strength in what? Squat, Bench, DL, Press, pull ups?? If so, how much? What are you doing now, and what do you want to be doing. I would start here. All the other things can be littered around it. We all want to be healthy and pain free, a good balanced program with certain factors included will do this but, consider this after you have the main goals drilled down.
Also, out of curiosity, how long do these sessions take you?
I'm not going to say you're doing too much because I don't know enough details and don't know what you're trying to achieve. You could do 10 exercises in 30 minutes with a light enough weight and short enough rest. If your goal was improving conditioning this could be ideal and fun due to all the variety. If it was getting a bigger squat then I would question it. I'd say just squat, and squat heavy, and add 2-3 assistance exercises, and this should take about 60 mins!
I think you may enjoy how Eric Cressey writes his programs. There's a lot more variety. A lot more "athleticism" (due largely to the variety). I prefer this myself to the likes of 5-3-1. As an example of what I mean, in his Show and Go program, you may do one main heavy squat in the low rep range, then a DL for speed, then 2 assistance, depending on the day, phase, whatever. Quite often it's just one heavy lift then a few assistance. The thing is, the heavy lift takes about 30 mins, and afterwards you feel like you've been hit by a truck. The thought of doing even 1 assistance exercise is daunting, never mind 7. Point is, you need to be productive with whatever you put in the program, and everything should have a purpose, as opposed to just "throwing a bunch of sh*t in the wall and hoping it'll stick".
I think you may also benefit in thinking outside of "your" box, just to get a fresh perspective. One example would be to look at Matt Z's log, and ask yourself what he's "missing". You're talking 3 exercises a session, sometimes 2, but he doesn't actually neglect anything. I'm not saying you should do what Matt does but, it's just good to go to the opposite end of the spectrum every now and again.
Basically, you're asking "why NOT", and we're asking, "WHY???".