There can be several things going on- how long since last repotting? A long time judging by the vines. Probably some soil problems complicating the issue.
My vote FWIW- when you water, take the whole thing to a sink, water until it runs out the bottom, tip the saucer too, then rehang. Now use the meter and see how it is after a week. or two.
Not sunburn. As WillC as has said many times, people usually overestimate the amount of light an indoor plant gets. Open the blinds.
Also check those stems with bad leaves- maybe just certain stems?
Bottom line, you can keep draping the newer stems over the old, pick off yellow leaves as they appear, and get a lot of mileage out of a plant like these
