I would say the key is when you said "faster, more technical stuff". Typically that is when people tense up. Working on speed IMO is a waste of time, speed develops on its own. Focus on mastering the technique at a speed you can play it perfectly, then as speed builds you will still be playing it correctly.
The brain only knows information doesn't know right or wrong just information. Example take a major scale, something we learn early on. But not knowing better we start trying to play too fast and make mistakes, seems harmless. Years later when playing a major scale after years of practice we still make mistake now and then, why? Because cateloged somewhere in your brain is a major scale you misfingered at some point early on. Your thinking I want to play a major scale and the brain just grab one of the bits labeled major scale, and boom its the one with the mistake. But if you learned a major scale even at a snails pace with no mistake the brain wouldn't have a bad version of one stored away. In fact every time you make a mistake you need to repeat that thing 100's to 1000's of times correctly to try and dulute mistake and hope it doesn't popup at an inopportune time.
Also as to the hand problem I've seen some have soreness because they aren't using a strap or misadjusted, or bass is neck diving. This results in you trying to hold up the neck at same time as trying to play. Last if you practice standing and bass is too low, that forces the wrist to bend too far and can to lead to all sorts of problems. Try raising the bass and dropping the left elbow to change the angle.
