I have a feeling that this topic has not yet been dealt with as it could have, so I will offer one more scenario on this gents freezer icing up.
If those door gaskets check out OK, then there is a good chance that the icemaker got stuck in the harvest cycle by a jammed cube. If this happens, and it is rare, the heater in the icemaker mold will stay on and cause heat buildup in the freezer. This causes the unit to run constantly due to the increased temps and also creates icicles from the dripping condensate close to the icemaker.
If you had experienced any hollow ice cubes in your bucket before all this started, then you need a new water valve on back to resolve the fill issue. As these valves begin to fail, only the first 7 cubes in the mold will fill, causing the icemaker to cycle prematurely. Usually the last cube is partially hollow, and the ejector fingers get stuck on them and jam the mechanism.