Another thought, following on Bjarney's observations. . .an experiment to try.
The field in open air around the motor will be fixed in orientation. Although the field is alternating, that is, expanding, collapsing, reversing, expanding, collapsing, etc., the orientation of the field, at a point in space, will be along the a line that doesn't change direction.
Imagine the iron filing - bar magnet experiment that uses a piece of stiff paper. The magnet is placed under the paper, the filings are poured on the paper, and then the paper is tapped. The filings line up along the lines of force. The shape of the lines of force is the same regardless of field intensity. The shape of the magnet will alter the shape of the field. In the case of the furnace motor, the shape of the motor doesn't change, so, the shape of the lines of force around the motor doesn't change.
Here's the experiment: Have the motor running and do a current measurement close to the motor, the way you have when you've noted past high readings. For this experiment, lets say that the direction of the wire that is in the clampon's jaw is the X axis of an X, Y, Z three dimensional axis for side to side, front to back, and up and down. We're going to bend the wire, but the direction of X, Y and Z won't change from the first way the wire was. While keeping the wire in the clampon, turn the pick up coil of the clampon ammeter 360┬║ along the X-Y axis and then 360┬║ along the X-Z axis. Watch the reading for a dip, or decline. This will occur as the pickup coil of the clampon approaches a 90┬║ orientation to the open air magnetic field from the motor. The motor field will be at some unique angle that most likely will not be along the X, Y, or Z axis of the wire. Placing the pickup coil of the clampon at a right angle to the open air motor field results in the motor field being "invisible" to the pickup coil.