Your original version reads fine to me. It's clear and unambiguous and to me that's what grammar is primarily for. So whether it's technically correct or not, I think it's ok. It certainly wouldn't bring me out of the story or anything like that.
Now if you're looking for the best sounding sentence that's a matter of aesthetics.
I'd probably go with EileenG's suggestion because it's more concise and that feels better to me, but that's about taste really.