This always is a problem in the unlawful detainer process: the lag time between the date when you get a judgment of possession and for money and the date that the sheriff actually returns posses-sion to you. This lag time is increasing in recent months due to governent budget constraints. That said, the answer is unchanged. You have to file another lawsuit, what I call a "post-posession" action. Typically this will be in small claims court. The good news is that in this suit you can ask not only for unpaid rent for those days between judgment and possession, but late fees and damage to the property exceeding normal wear and tear, all the things you wanted on your eviction action but couldn't get. In the roughly thirty years that I have been doing this, I cannot recall a single such suit. Perhaps my clients take my advice and bring the action in small claims.
As for amending your judgment, forget it. The judgment was correct at the time that it was entered, and the Court gave you all that it could at the time it was entered.