Could price floors improve worker safety in the meat cutting industry?

A priori this is difficult to say without any empirical experiment but it is unlikely due to:

1. Price floors do not necessarily lead to more competition on quality. Theoretical models do show that price floors can (depending on parameters) lead to an increase in quality (Bilotkach, 2012 and sources cited therein), but they can also just result in intensifying competition along different dimensions (such as location, advertising, and other dimensions without necessarily more differentiation of products (see Bhaskar (2003) and Bilotkach (2012) and sources cited therein).

   So already an issue is that price floors cannot be guaranteed to lead to higher completion on quality. This would first have to be tested in the specific case.

2. High-quality products do not necessarily imply better working conditions and high safety standards. Apple products could be argued to be of high quality (although I am an economist, not an engineer), yet apple is getting regularly lambasted for poor working conditions in its factories (see this article from the Guardian).

   I was not able to find on google scholar any empirical or theoretical work that would support the idea that price floors on products would lead to better working conditions. Also higher firm profitability is not necessarily associated with better working conditions. Firms can as well just keep working conditions the same and pocket higher profits.

3. Even if it would work in public economics we are not interested in solutions that just work, but the solutions that achieve goals that we set in an efficient manner. As mentioned by BKay in their excellent comment there are many different ways how to raise work safety, arguably most if not all ideas mentioned in the comment would be more efficient than price floor which would likely have to change with market conditions and be set in a careful manner which might be too difficult to implement.