You made an offer to mow it for free, in exchange for the fees. Is the property what a $200 a month contract should be? Are you sure wou wont be expected to do other things around the property? such as pick up trash, blow dirt out of street in common areas? That all cuts into your time. You said you can't afford the $200 a month, but you can afford to instead give away $200 a month in service? Why not go pick up a couple more accounts instead with that time, even if you picked two lowball (no im not condoning lowballing) accounts that are $25 a week, that would give you your $200 a month you are looking for.
Another thing many people don't think about when bartering is that it is income you technically earned, yet can not claim as income. By them paying you the $200 a month, and you paying them the money right back, it will show that you made an additional $2400 over the year in income. Of course though you would be taxted the income as HOA dues are not tax deductable. We often have contracts offer to barter with us, a few months ago we did some sub work and part of the pay was a trailer the contractor was selling. Rather than taking the $3k off the bill, what we did was I paid him for the trailer and he then paid me for the job. Yes technically, we had bartered the trailer into the price, but as far as our bank records show and taxes are concearned, we were paid for the job and bought the trailer. Doing it this way, that $3k still shows in our net income.
Why do people not respect us as they do other tradesmen? Because every Tom, Dick, and Harry doesn't think he can be a plumber or electrician!