Looking for feedback on my opinion here. It could be pretty naive as I'm no expert.
Instead of working under your employer while trying to convince them to give you the pay and rights you desire, you could just quit and be self-employed and then negotiate for the same rights and pay.
This probably wouldn't work in a single case, but like many things, if enough people do this, it would be very effective. If you can coordinate enough people to strike, you can also coordinate them to set their own rate and figure out how much they think their labor is worth. They would be doing that already in order to unionize.
With many people offering their labor in a business to business transaction at a certain rate, you are setting the market rate for that labor. One downside I can think of is that you would be subject to self-employment tax of about 16% (in the U.S., at least). But this tax can be passed to your employer to pay by raising your hourly rate by the same percentage. I don't think there could be laws passed that prevent people from doing this without interfering with the general right to start your own business.
You wouldn't have to scale this down to the individual level. You could go into business with people you like and trust, and your company could sell the labor of its workers for some price you all agree on. Then perhaps it's cheaper in this way to get health insurance. This works even across industries. Not everyone has to be in the same field to get the benefits of going into business together.
You would effectively be creating a staffing agency with 1 or more members. You negotiate your own pay and the times you are willing to work. Plan for a number of sick and vacation days and then factor those into your rate. Do the same with insurance costs. Basically, just ask yourself how much you want to get paid. What is a livable wage? Or maybe you want a more than liveable wage? Don't sell yourself short. Then pass all your costs of doing business to your employer. The only upper limit is if your employer is unable to make these payments because it's an unreasonable number (unreasonable as compared to their cost of doing business, not their profit margins or greed).
The market rate is generally going to gravitate toward the lowest available price. So work with your peers in the same market to make sure the lowest rate is something liveable.
Any immediate flaws you see with this plan besides the effort involved in coordination? This way you can use the existing laws to end up with the same result as unionizing, rather than try to force the hand of a government or employer who are resistant to helping people. Obviously, your employer can also choose to just not hire you, but if enough people do this, they don't have much of a choice.