Unfortunately if this is the case, I imagine it would still be the case even if food truck vendors were forced to submit a form testifying they had proper disposal arranged. As a thought-experiment, I imagine if this food truck was dumping his garbage in the mayor's garbage-bins, that they would find a way to make him stop with existing laws on the books.
There are usually laws on the books that could be used that simply are not enforced. Many jurisdictions have (by)laws about citizens being allowed the "private enjoyment" of their property, and you could easily claim that's infringed on here for the reasons you laid out. Public nuisance laws are also, by design, incredibly broad.
My point is that I believe it's a problem of enforcement and political will; not of letter of the law.
Where I am from (Canada), the correct remediation would be to take your landlord to the tenancy courts where you could represent yourself (i.e. not need a lawyer), but that's still undeniably a huge pain for a rough situation. I'm glad you're in a better spot now.