I was in a similar situation last year. However, my university does not allow the CPT for the last semester or the semester which you are graduating. I had an interview on sept and was asked if i could join in October. As you know it takes about 90 days to get the opt these days so it was not possible. My employer suggested i talk to my DSO about CPT but i was told CPT is not allowed for the final semester.

Now, the precompletion OPT takes almost same time as regular OPT. If you are doing thesis-based masters then you can defend as soon as you can and once you finalize the defense date, you could apply the OPT ASAP.

If your masters in non-thesis based, and you have to take some class in summer then I think you cannot start OPT before the end of summer semester. BUt you can apply 90 days in advance.