Injury reduction ideas for a reluctant workforce?

We are over our corperate cap of number of recordables for the year and we still have 3 months to go. I have been tasked with coming up with ways to reduce or stop our injury trends. Any helpful advice is appreciated. Last year we had lacerations and contusions. This year 90% of our injuries are strains or sprains from overexertion. Keep in mind that we hire anyone who is willing to work. If you can write your name and push buttons, you're hired. I don't say that to be mean, it's just fact and gives an idea of the workforce we have.

What has worked at your location to improve early reporting of MSDs? We do daily tool box talks so operators have a time to talk about safety with theit supervisors, is there more we can do during this time?

How can I get employees to stop "power through" the stiffness and pain so that they can get early treatment and not have it become a recordable? He have an onsite PT 2x a week that is available to anyone who needs or wants him, even if it's not work related.

What more could our supervisors be doing to be proactive and not reactive? How can I get changes to last and not fall off after 2-3 weeks?