Turning a deaf ear is pretty normal at around this age apparantly, - Humphrey's just 13 months and we're having to go back to basics on quite a few things. Its not that they're deliberately being disobedient but once there's a distraction, particularly a smell, they literally just switch off. I have held a particularly tasty treat on the end of Humphrey's nose to attract attention and he's ignored it, its as if he's on another planet.
I watched a programme on television recently about having dogs neutered and while many believe it does alter the behaviour, others, including in this case a veterinary professor of medicine, claim that it doesn't, - there is also a voice that claims the hunting instinct increases.
Our trainer suggested using a long (10 meter) lead for a few weeks. I had a lot of reservations and hated the idea of limiting Humphrey's freedom as, like you, I loved to see him enjoying himself racing around off lead. However, lots of people here also recommended it so we tried it out and for a couple of months we used it consistently, training whistle recall at the same time. Every time he turned around to look at me or came back to check in, I praised him. After a couple of weeks, I let the go of themend of the lead and he dragged it behind. He's now off lead again and very rarely strays too far.
Personally, I'd consider giving this a go before you resort to neutering, - unless ofcourse Dixie has any other medical issues.
Best of luck!