I was diagnosed earlier this year with Thyroid cancer, along with 2 other pilots in the Seattle area. One just finished his treatment this week and think and the other got his 1st Class medical back last month about a week after finishing treatment. So it does not seem like the FAA is taking very long to issue an SI for Thyroid cancer. I will find out in a few weeks when my treatment is finished.
They did tell me that I would likely get a 6 month SI for a year, then a yearly SI for 5 years total. Seems to be the standard.