If its taking a week to drain a PP3, then the leakage current is under 4mA (3.57mA for one week is 600mAh. It looks like the board has 10mil or 16mil traces, which are 19 or 12 milliOhms/cm respectively in 1 oz copper, so at best you'd be getting around 70uV/cm along the trace that's got the excess standby current. Thermal EMFs are a real problem when you are trying to measure uV so even if you've got a great bench meter that can resolve down to 1uV, probing along the power lines is unlikely to work well, if at all.
Unfortunately high standby current is typical of MCUs that have suffered ESD damage to an I/O pin that hasn't quite killed it. If that's the case, unless you have the full firmware image, a spare MCU and the correct hardware tool to flash it, you are FUBARed.