Congrats on doing weighted dips. It is one of my favorite movements and I never see people do them.
I get what your saying. I am a performance coach by trade and it is nice to see someone who is into functional strength versus just getting a big upper-body so they can wear tight shirts to the club.
Just food for thought, for the last year I have been experimenting with some minimalist training (less is more), for sake of my nervous system because from years of doing those movements you mentioned, I built up a lot of neural-fatigue (I am a USAW coach so I used to Squat, Deadlift, Press, Clean, constantly) and got to the point where I was less happy doing those movements and more prone to injury. I still do many of those movements, I just take a very different approach.
Since i've been focusing on a minimalist approach for about a year, I am now about twice as strong as I have ever been and my strength feels much more functional than it has in the past. There are some cool sites that give you a little background into it if you are interested I can pass along.