Hey there, welcome to the forum.
I too have worked in and still do consulting for government entitiies and I know how it is in "hostile" IT environments. InfoPath is a great tool for forms and a liberator for knowledge workers and employees in government if you can get the few things you need.
Ideally, best practice for an enterprise solution such as this would be to store the final data in a backend SQL database and use web services Qdabra Database Accelerator Suite Version 2.1 - Developer, but this would require IT involvement. In some cases, the powers that be have made this happpen, in other cases, departments have put in their own "dedicated workstation" (server) to accomplish this themselves.
I would recommend an intermediary solution, get something going rapidly and get your proof of concept so you can lobby for doing it right later. It won't be as good or easy as doing it right the first time but that is the whole philosophy there anyway right? :)
So I would create an Access database with all of the fields you need. It can be one table or a parent table with one or more child tables. You should have a file share or SharePoint or somewhere you can put this table where everyone can access it. Not best practice but your only option without a server. Create a new InfoPath form as a database type connected to your Access Tables, use the design views and layouts to make it wizard like for the data entry, to give the info collectors happy. Create a second view in your form for the data checkers or the next process or it could be another form. Last make a summary view, a repeating table of the data for the "report" and the analysis. Also you can setup a spreadsheet that connects to the data and allow people to analysis the data that way and just the input can occur via InfoPath.
Otherwise if you need some consulting to either train you or help with the project you can purchase some support credits on the http://www.qdabra.com site.
Good luck and have fun.