Are there any open-source software solutions designed specifically for the money transfer industry?

None are available, in so far as I know.

There were a few attempts to have this going, but no progress was made. A few commercial vendors have put out a free version, which is nothing more than a watered down version of their commercial packages, hoping that by using the free version you might upgrade, but even then, the software is not open source. There is Cyclos, but its used more for closed networks for payments (mini banking), but its never been modified for use by MTOs.