I have some extremely tight upper back muscles that seemingly no amount of stretching can loosen. What are some alternate or supplemental approaches I can take to loosen tight muscles outside of the typical stretch routine?
Upper back tightness can be caused by weakness and/or bad posture. I'm a Pilates's teacher and most people I see with soreness in the upper back area often have weak deep neck flexors and weak upperback muscles (a muscle can be both weak and tight). Stretching or foam rolling will be good to release tension but it could be useful to find the underlying cause of your tightness. Upper back muscles work all day to hold back the head, especially if your head is protruding or you have hunched over shoulder from having a desk job or using the computer a lot. They are contracting while being extended which happens to be the most demanding type of muscular contraction (eccentric contraction). Strengthening those muscles will help you keep a better posture which ultimately leads to less strain.
If you don't have acute pain at the moment, I would suggest you work on strengthening your neck flexors and upperback muscles. Try 1 or 2 series of 10 repetitions of these exercises every other day.
Most people have weak upper back muscles so there's no harm in giving those exercises a try. Go slowly and stay within a painfree range of motion. If the exercises aggravate your pain, stop and seek out a physical therapist consultation.
Also, if you do have a desk job, try rotating your shoulders towards the back for about 30 seconds every 30 minutes. This will bring blood flow to the area and help get rid of "muscular contraction waste" that get stuck in your muscle when you keep a static position for a long time.
A pair of tennis balls are your back's best friends. You can stretch and release the spinal erectors by rolling up and down from base of the rib cage to base of the neck along the outside of the spine. (Some people lie on two at a time, I like to do one side at a time.) You can then work on the lats/shoulders by starting with the ball outside the spine then sort of rolling over like you're rolling up onto your side and the ball goes toward your armpit, and work your way up and down the back doing that.
A good Yoga or Pilates teacher ought to be able to teach effective techniques for this. A google for 'back rolling tennis ball' also gets results.
For a more formal documented solution, this is of course a for-profit product, but, it works:
Foam rolling from the base of the rib cage to the shoulders can also be helpful, as is lying on the roller lengthwise and just relaxing your spine into it. But it's harder to target specific back areas with a roller.
Before attempting some of the very good solutions proposed, be sure to get a proper sports and remedial massage with a qualified therapist. This will help to identify which muscles are causing the tightness (it can be indirectly from other, seemingly unrelated muscles), help to lengthen and soften them, before you begin to work on them yourself.
There are some amazing techniques in sports massage that can immediately give you more flexibility. PNF is one of them (PROPRIOCEPTIVE NEUROMUSCULAR FACILITATION).