I decided to go for regular headphones, closed-back for sound isolation and bluetooth as wires are a pain. After a lot of research, the only headphones that met these requirements, with an emphasis on staying put on the head while lifting, seemed to be Plantronics BackBeat Fit 6100 and JBL UA Sport.
https://www.amazon.com/BackBeat-FIT-6100-Headphones-Water-Resistant/dp/B07WHF6LLG