Hey Jessie and welcome to official membership!
I hope your enjoying it so far! On managing the scripts constant fluctuation, here's some thoughts and I hope they help you. If you have any more questions that I might be able to help you with feel free to reply/private message me and I would be happy to answer them.
1. Line Change Sheets- This is basically an excel spreadsheet that lists all the changes in the lines to keep the production staff and cast up to date at all times. I'll try to attach a copy of what I use in school for a line change sheet although you could also google it and get a more detailed example.
2. Backing Pages- Some stage managers use a backing page in their script or they just use a blank page on one side of the script. If your right handed hole punch your pages on the right side so that the blank side of the paper will be on the right side making it easier to write. If your left handed hole punch the left side for the same reason. You can search the internet to look for more information about backing pages because they work for some shows and sometimes they don't.
3. Detailed Rehearsal Reports- The more detailed your rehearsal reports the easier it will be to send out info and keep everyone up to date on what's going on/any changes to the script.
4. Try to keep an updated copy of the script in word/on the computer if you can. I know this is not always possible however it's nice to be able to keep an updated script in the dropbox so that you could print out the updated version for the designers at tech. (Make sure that they have the same page numbers as yours)
That's what I could think of that might help fix that, and I hope this helps you.
~Caroline