“Their best leverage is when the singles come to meet them initially,”
Let them use it. Plumbers and electricians do.
“but as stated above, shadchanim don’t do so because they aren’t comfortable doing so,”
As are many new plumbers and electricians, and they end up in disputes with their customers as well.
One can not expect to deal with people throughout a process that can take months and months, as as advisor, a friend and confidant and then suddenly at the end of the process it is suddenly a business. If it is a business transaction as codified in halacha, then let a contract, written or oral, be drawn up upon commencement of services. Both sides will stipulate what is expected from the other, and this way there will be no misunderstandings.