The problem, though, is that whatever styles I apply to the individual layers within the linked gdb does not "stick" to that layer. When I save the project and re-open it, all the style information is gone; the layers have reverted to the default gray colors and fill patterns.
Correct. ESRI GDB cannot store Manifold style info. GDB also is not a general purpose DBMS (like Oracle, MySQL, PostgreSQL, SQL Server, Db2, etc) within which Manifold can create additional tables specifically to store style and other meta info.
If you want to leave your data linked, what you can do is to follow a procedure similar to that shown in the Example: Style Applied to an Image Server Image topic. In that topic you re-style an image coming in from a server which is read only and into which you can't upload style info about Manifold. But you can copy the image (not the table, just the image) from within the data source and paste it into the Manifold .map part of the project.
[Note, by the way, that this has nothing to do with the system data folder. See the illustrations in the Importing and Linking topic in the "portals to other worlds" section. The read/write portion of your Manifold project is everything that is outside of data sources that are their own limited worlds, like read only data sources or data sources linked from formats to which Manifold style info cannot be saved.]
Suppose you link to the Naperville gas sample GDB that ESRI uses in tutorials. Open up the Landbase folder in the data source and you'll see a Tax Parcel table and a Tax Parcel Drawing. Copy the drawing.
Right click somewhere outside of that data source, like in the main part of your Manifold drawing and Paste what you copied. You'll have a copy of Tax Parcel Drawing that takes its data from the Tax Parcel table inside the GDB.
You can style that Tax Parcel Drawing in the main part of your project. Save the project, and then you can close it and when you open it again the Tax Parcel Drawing will still be styled. Why? Because it's a drawing in the local project where style info can be saved for it. All the data is still in the GDB, because drawings don't store any data in Manifold... the tables do. A drawing is just a viewport that says what table to get data from, what the geom field is and so on.
Suppose you want to use that same drawing in a different project? No problem. Open up your saved project with the Tax Parcel Drawing in one Manifold session and then open your different project in a second Manifold session. Copy the Tax Parcel Drawing and also copy the Naperville GDB data source, and paste both of them into the second Manifold session. Now you have your styled drawing and you also have the data source to which it refers.
Sounds like it would make a fun video. :-)
Ah... almost forgot:
I haven't imported the gdb files directly into M9 due to the excessive time to open each database each time I open the map file.
That doesn't sound right. If you imported the GDB into your map file there is no connection to the GDB and there is no excessive time to open any database. If your data is imported into the map file it pops open in 1/10th of a second, faster than a link to the GDB (GDB is far slower than Manifold .map format).