Orthogonality (as the O in OFDM) guarantees a fixed phase relationship for every symbol unless a pattern is introduced in an effort to reduce peak to average power ratio (which I do not believe is happening here). PAPR is bane of OFDM and much research has gone in to reduce this problem which requires high linearity in the amplifiers in cell towers. Linearity is typically accompanied by poor efficiency (lots of heat goes along with watts).
In addition to this , there is indeed a random process involved in the synchronization. Schmidl-Cox is imperfect and "fine tuning" of the sampling phase also has some randomness. On the air you will have phase offsets due to frequency dependent group delay through the analog components of the RF systems, group delay due to multipath, and on and on. I didn't open your grc file but I assume this was the perfect "wire" channel with additive noise in which case ignore all of the other analog stuff I added.
Bob