This isn't a tool problem. It's a process problem. The solution is to make the costs of the current process visible to your management team.
Analysis and Recommendations
You don't identify your role, or that of your boss. Nevertheless, for most of your issues you point to your boss's decisions and company policies to explain why data reconciliation is a manual process. Processes have an associated cost, and the time spent reconciling all those Excel spreadsheets is one of them. Those costs, as well as any process improvements that could cut costs, should be visible to your management team so they can make an informed decision about whether or not the current process is optimal.
By definition, management owns all costs and risks related to a project. That includes the responsibility for budgeting for capital costs such as purpose-built tooling or other process automations, or opting for semi-manual processes such as the one you have now. In either case, management is making a business decision as to which costs they prefer to incur.
Making the costs (including everyone's labor to fill out the data, as well as your labor to reconcile it all) and risks (manual processes are often error-prone) fully visible to management supports better executive decision-making. Making potential quality improvements or cost savings visible to management gives them options about where they want to invest business resources. If you make a case for a different process or tool that can save the project money, management can then decide whether or not to implement the change based on the needs of the business.
Whether senior management applies resources to improve your process or not, they still own the process. That means they must explicitly or implicitly accept the costs, risks, and consequences of whatever business decisions they make.
The project manager role shouldn't be held responsible for the choices of senior management. In this type of situation, the responsibility of the role extends to making known issues and potential improvements visible, and then gathering a funding or implementation decision (which may include acceptance of the status quo) from project sponsors or the accountable executive resource.