Correction: SqlExpress is not "file based". It is exactly the SQL Server with some features stripped, such as analysis services, reporting services...It is installed to your computer as services, which can be accessed from other computers in the network, if configured properly.
It seems the OP really need Excel's built-in computing power, thus, choosing any other data storage would require home grown computing features to be incorporated. And yes, with SQL Server/Express, stored procedures would a good tool to build internal computer function into the data storage.
The original question (rather, questions) is really difficult to respond because the main objectives are not that clear: if the slowness is the main concern, using data link to populate table from Excel obvious is the cause. So, the question is: does the sheet in Excel do a very complicated calculation that it is very hard to be developed/programmed in other means? In most cases, it would be not, I'd say.