You can ask on the IRS to make a determination with an SS-8 and file a form 8919 to get back the part of the SE tax that the employer should have paid.

Note that "hourly" payment is not inconsistent with being independent contractors. Lots of independent contractors (even lawyers) bill by the hour.
There are a number of factors that determine if you are an independent contractor or not. Information is available here:
https://www.irs.gov/newsroom/underst...or-designation
However, I suspect that you are indeed an independent contractor (even for the "hourly" work) based on the way your job is handled. There's no requirement for a written contract.

How valuable to them you were is largely immaterial. There's nothing illegal about exploiting people like this.
The asbestos exposure you may be able to follow up with OSHA or the state DEQ.

You don't get damages unless you have an actual injury. You don't get punitive damages just because you're upset.