You got almost everything wrong.
First what you got right. Gaetz did resign his current Congressional seat. He did not resign the seat he was elected for. That means on January 6th, he will be sworn back into office. There is not enough time between then and now to have a special election.
He will be sworn into office on January 6th, and could not have been actually nominated until January 20th, so his stated reason for resigning from current office makes no sense. The real reason was he was hoping to be out of office before the report for his removal from office was released.
Now Gaetz is hoping that the previous report for removal of office will be considered stale for his "new" office, and have to be completely redone. That will buy him a few more months, and he may be able to keep witnesses from testifying against him again.
It is a coins toss on how long he will remain in office, but he will be sworn in on January 6th.