Sharing Workbook With Multiple Users Entering Data Simultaneously

My Workbook contains several UserForms in which employees will be entering hours and activities on a daily basis. In the UserForm, they select their department and enter hours for each specific type of work/activity that shows up for that department in the userform. They click the submit button and all the data (date, name, department, type of work and hours) is added to a database table in another sheet, which in turn feeds a number of reports.

I need to be able to have anywhere from 20 to 100+ employees enter their hours on a daily basis, many of them at the same time, all from different locations (within the network of the client's system), using the same UserForms.

We've experimented with Google Drive, but that seems not to be the solution. It kind of works, but is not secure (it installs a copy of the entire workbook on the users system and then synchs the data back to the server upon "save") and way too cumbersome. I've heard of SharePoint, but not every client has that installed (and frankly I don't know how it works).