Slightly increase scope: include payment requests

The project should really include outgoing payments along with it.
Submitting an invoice for payment as an external party is really just a
"base case" of a reimbursement request.

The only complication I can imagine this adds is allowing the general
public to create an account on the system, or allow for anonymous
submission, which might lead to spam concerns in deployment.

I believe these issues should be easily mitigated and will not
drastically increase scope of the project.

As part of this actual change to the text, some wordsmithing and changes
throughout to s/reimbursement/outgoing payments/ and other similar
changes are made.