Internet of Things (IoT) deployments are projected to reach 30.9 billion by 2025, most of which will employ little or no encryption. Specific Emitter Identification (SEI) is being put forward as a lightweight security approach intended to solve the risks of unencrypted or weakly encrypted IoT deployments. SEI exploits waveform distortions that are intrinsic, distinct, and imparted during normal device operations, which permits the employment of SEI without needing to modify the IoT device. However, SEI performs very poorly when the waveforms used to train it are collected at a different time from those it is being tasked with classifying. A solution to this cross-collection problem must be found before SEI can be deployed as a viable IoT security solution. This paper assesses cross-collection SEI when waveform time offset is and is not present, the intentional waveform structure is removed, and SEI is performed using handcrafted and DL-based approaches. The results show removing the intentional waveform structure improves SEI performance by as much as 8% versus using the raw received time domain samples. The results also show that cross-collection SEI accuracy is highest when using a Graphical Neural Network (GNN).