(Edit, adding reply to @nickclube: Now what you suggested makes sense to me as I have used the "Import Song Data" option and found it to bring in everything except the busses. Seems like a flaw. I do hope they fix that in an update.)
Thank you both for answering. @LHandley, this would definitely work, and I have used this before. My question didn't do a very thorough job explaining what I was looking for though. I was thinking that when you are in the New Song dialogue window, you might be given a fourth tab of previous .song files to use as a template. HOWEVER, your answer here got me looking back into the question and I discovered a wonderful feature in Studio One that does exactly what I'm looking for, only better! It seems like I'd seen this before on a YouTube tutorial but had forgotten about it. Here's how it works:
Create a new .song file that is blank. In the Files tab of the Browser on the right, navigate to a previous project, right-click the .song file, and choose Import Song Data. (Alternate method: Song menu at top > Import Song Data, and browse for .song file.) This brings up a fantastic dialogue window where you can import a single element, every element, and anything in between for an existing project. AWESOME! Besides that, I had seen and used the method of spinning down the triangle icon beside the .song file in the Browser and pulling in individual elements of a .song file. I already had my mind blown when I discovered that!
So, I'm gonna consider this closed. @PreSonus, if you want to add a fourth tab to the New Song dialogue window that basically takes you to the Import Song Data dialogue window, that would be neat. It might help people discover that option more readily. But at this point I feel that what I wanted already exists. Kudos to you for the excellent DAW!