Looking for advice

I have a workshop that has an old Technics receiver in it. I mainly use it to listen to the ball game while working (yes, I’m that old lol). I also have a fire pit outside near the workshop where I stream music from my phone onto a small portable BT speaker. But I would also like to listen to the game out there (games are only broadcasted on FM signal due to contractual issues between team & radio station). I would like to find a cheap way to consolidate what I’m doing. I was thinking of hardwiring outdoor speakers to the outside of the workshop and connecting a BT transmitter to the receiver. I think that’ll allow me to play the game from the receivers FM signal outside or stream music from my phone to the transmitter, then out to the speakers. Does this sound plausible? Any thoughts or suggestions (keeping in mind I’m trying to do this cheaply)? Thanks in advance