student visa expires on 15th but completion letter will be available on 18th

Hi everyone, I am waiting for my completion letter to apply for my TR VISA 485. The problem is my student visa expires on 15th and completion letter is supposed to come on 18th. i have request my uni but they cannot guarantee it. Is applying for visitor visa and then applying for tr on 18th the best option? I have got all other documents for this.
The agent i am talking to is advising to apply the visitor visa and wait until the completion letter to apply for TR 485. the problem here will be, I will get bridging A for visitor visa which will switch to bridging C once i apply for my TR which probably means i have to quit my job?
Does anyone have any experience on this front?