Possible reasons:
-Temperature at the top of your fridge is warmer because cold air sinks and because the 2x4s that we all use in these freezer conversions have an R-value less than half that of the rest of the freezer, so it is warmer near your lines. This releases CO2 out of solution. If you have temperature probes, check your temperature differential from the bottom to the top of your fridge. If it is a big difference, consider adding a very small fan inside to circulate the air (like a 3" diameter).
-Warmth transmitted through the taps to the beer directly next to it. Not an issue (and not much you can do about it) unless your beer lines go downhill towards your tap. That beer will warm and release its CO2 away from the tap.
-Make sure your collars are really tight. If they are not, the tap may not close all of the way.
-Coil your lines so they are uphill all of the way to your tap.
-Dropping your pressure for serving will cause more bubbles in your line, not less. Think about it - if you lower the pressure from the amount at which it is carbonated, the carbonation will want to leave the beer to equalize. The CO2 that leaves will seek the highest point, and that will almost always be in your lines. Many people lower the pressure to serve because it comes out too fast and foams. The correct solution is to do what Drunkensatyr and FlyGuy say and use 3/16" lines. This allows you to run at the higher pressure that you store your kegs at because the restrictive line will scrub off that pressure and give you a perfect pour.
The solution: balance your lines. There is a perfect balance that can be achieved between temperature, pressure, the resulting carbonation, line diameter, and line length. Download my Beer Line Length & Pressure Calculator and you're on the way to a solution:
https://www.homebrewtalk.com/showthread.php?t=35369