Sync many client database to one central database
It seems to me that you're falling into an XY Problem. You want to see the data from lots of different databases, and have the mindset that you should only connect to a single database. That line of thinking logically lead you to the conclusion that you need to bring all the information into one central database. 

IMO your real problem is needing to see the data in multiple databases in one application.

One way to accomplish this is to merge the separate databases back into a central database like you suggested. Since you aren't looking to modify the existing clients to use the master database this seems like a complicated and error prone plan that will increase your maintenance costs. 


You have to figure out how to merge separate databases without conflicts.
You have to worry about performance tuning the master database separately from the clients since it is going to naturally have much more data than any single source database.
You are artificially increasing the storage/hardware/licensing costs by creating a master database that is only going to be used by a small number of users.
While the space/size constraints of SQL Express might work for the client databases, once all the databases are pulled into the master database the combined total might overwhelm SQL Express's constraints.




I would recommend you consider taking a different approach. Instead of concentrating the databases why not concentrate the connection strings? Following this route you would only have to write a screen for the admins to select the project and then perform a lookup for the correct connection string for the project's database. Then you would be able to essentially use the client but dynamically swap out the connection string depending on what database is being targeted.