The best way to share a large Translation Memory is to use Trados Live Team or GroupShare.  These applications are designed to share and work on the same TM by hosting it on a server for this purpose.

If you are working with the desktop version of the tools then I'd recommend you create your projects using a Project TM and not your Main TM.  The default does NOT use a Project TM:

But if you use the "Prepare" task when you create your project instead it will create a Project TM for you:

The Project TM contains a subset of your Main TM with only translation units relevant to your project.  This will be much smaller and when sending out the project as a package, or as individual sdlxliff files you can include this smaller TM.

In principle these settings control what translation units will be added to your Project TM: