In the omegat.prefs file, you can change the value for the parameter most_recent_projects_size, to let's say 10 instead of the default value 5. This allows you to have a longer list in OmegaT in the menu entry:
Project / Open Recent Project
I would like to be able to change this value from the Options / Preferences dialog
Honestly this is exactly the kind of fiddly preference that I feel shouldn't be taking up room in the GUI; instead we should have a default that most users are happy with, and a way for power users to change it if they want. We already have that. However I agree that 5 is too few; I will increase it to 10 along with some other improvements.
This sounds like a great solution. Cheers!