I'm not a barn owner, but what you are describing is typical in any labor / service industry.
And, you can allow people to work off their board. You just need more structure.
You can go hourly or per diem with this recommendation. I recommend per diem.
First, create a checklist of things that must be done when cleaning a stall. Don't forget to describe/define the quality standard. A clear photo of a properly cleaned stall may be a good idea.
At the top of your checklist, include the spots to write in the following information:
Stall number (or other identifying detail)
Date and Time Started
Date and Time Ended
Quality Checked by Name
Date and Time Quality Checked
Score: Satisfactory, Needs Work, Unacceptable.
Then, you and one or two other people (preferably inexperienced people) perform the checklist, each on a single stall. Time each person.
This is your baseline. If you took 30 minutes but the newbies took 60, then you should know that a person should originally take 60 minutes, but with time and practice may be able to knock it down to 30.
Now, place a value on that stall. Is it worth $5.00? $10.00? What is it worth it to you to not do that task.
Now, implement it. Let's say it's $10.00. A squosh over minimum wage, but a nice round number.
Sally wants to work off board. You tell her for every stall she cleans you will deduct $10.00 from her board. You tell her she can work on Wednesdays from 1pm to 4pm.
When she arrives to work, you hand her the first stall checklist and date and time it. She completes the work. You inspect it. Passes? Move on. Doesn't pass, communicate the errors and let her fix them. You don't sign off a form until it meets the photo (and you have to be fair here).
At the end of the day, you tally up the number of forms she has that are "satisfactory.". That is the amount deducted from her board.
Your problem is nothing unique to you; it is a people management issue.
You can't expect to tell someone to clean a stall and they will clean it to your expectations. You know your expectations and you are willing to modify them based on circumstances. An employee can't know these things. They can be taught these things.
Even if you did say, "do this, do this, do this" a lot of people have problems remembering those details. Technology has ruined us from having to learn and retain.
Adults, especially teens, should have no more than 2 details or instructions provided to them verbally during the learning phase.
Also, cleaning is a subjective opinion and very biased. I have a level of clean that may differ from your level of clean. Are these people really trying to screw you or do they just have different ideas on what a cleaned stall really is? The latter is my first guess. As word gets around that you were not happy with Sally's work, Greg will spend more time doing unnecessary things to try and please you.
Take this for what it is worth. Your problem is a people management issue. Add structure, feedback, and a way for the person to measure themselves and you will find your workers will stop and review the objectives before asking for a critique. The form helps your bookkeeping and let's them know you are being fair and honest.