... the software is something of a "monkey's paw", since it catalyzes a process that requires additional hw/sw/services.

Nice trick if you can pull it off. It depends on how canny your target audience is. Selling consultancy on the back of a loss leading software package is standard practice, and justifies how many of us can spend work time on open source projects.

Would open-sourcing this to get feedback from developers help or hurt, and would anyone even contribute if their suggestions go into a product that benefits me financially?

That depends precisely on the kind of licence you issue with the software. It is worth looking at existing licence templates, such as the GNU General Public Licence, and the Artistic Licence - and others.

In terms of your dilemma - to open source or not to open source, this is a question of the tanstaafl argument. If you want to charge for your software, people working for you will expect to be paid.

As for governments, might there even be legislation in the U.S. which discourages/forbids governments from colluding with each other in areas where the private sector can be expected to provide?

I admit my ignorance about the American due process when it comes to government procurement. The situation in the UK is quite different, as authorities do tend to work together, at least in principle, in the collective aim of saving money.