I worked quite hard on this problem for a while, and kept him on a 32 foot line apart from for short bursts of offlead where I felt there was a decent chance of being able to get him back promptly. I carried roast chicken with me wherever I went! I made a huge effort to get him playing fetch and tuggy with his special Kong Tails that he's only allowed on walks, so that engaging with me would seem interesting and fun. (hah! dogs are easy to fool... )
Then Az got ill, and suddenly things became more complicated. I really needed to be able to exercise Brythen properly, so he would not eat too many shoes, daleks, curtains, beds, expensive books etc. But Az desperately wanted to come with us, and he got tired terribly quickly. Although I sometimes walked them separately, I ended up quite often taking Brythen to places where he could hare about after rabbits for ages and I could walk gently for a short distance with Az, and then take him back to sit in the car while I waited for Brythen to decide he'd had enough. This strategy is not ideal, but sometimes, needs must.
I have been quite thankful for the rain. Brythen HATES rain and mud with a passion, so has been much easier to keep a handle on than he might have been. There have even been a couple of days when I've taken dogs out for a microwalk in the morning, which was abandoned due to lack of enthusiasm from all parties. Then I haven't been able to stir them out of bed for the evening walk at all. Which, given that Brythen in good weather will basically run until there is no more land left to run on, is not bad really.
I think the long line walking has helped - or maybe he's just growing up and forming more of an attachment to me. He's less likely to head off to the hills now - he does tend to hang about where I can see him, and quite often, he comes back when called, or spontaneously come up to ask for a game of tug! But he's still very unmotivated by food (I shoved a pile of dried chicken liver under his nose this morning and he totally ignored it...)
And of course, sometimes there are the walks like this evening's walk, when I carefully walked him all around some fields on his longline, only to have him decide to throw a tantrum when we got back to the gate, wriggle out of his harness and disappear after the elusive bunnies. I'm afraid I did lose my temper and grump at him a bit after that, which I always regret afterwards. He just shuts down and try to keep away because he knows from early experience that angry human beings are just violent and incomprehensible, and it doesn't even occur to him to try to change behaviour as a result.
I never have had much time for long lines before, because Mollydog was a nightmare with them - give her a few feet of rope and she would inevitably tangle herself up into an unsolvable melancholy greyhound-knot. She was very food motivated, so it was relatively easy to get her to be very reliable offlead without using a line. But I am finding it handy for Brythen, who is much better at picking his paws up and not getting the line wound round his legs. He's also rather more erratic than Mollydog ever was!
The big problem with using a long line around here is that the open areas tend to be all heather and gorse, so you just can't let the dog trail the line or he gets snagged almost immediately. I've been using it on the quietest areas of lane instead. OK the tarmac is filthy and full of potholes, but it is possible to practice loose-line walking there, and I can hear the occasional cars coming in plenty of time to reel him in.
Brythen still hasn't come anywhere close to catching a bunny. I'm not sure he'd know what to do if he did actually get within grabbing distance of one - his idea of fun seems to be staring longingly, then galloping about madly in a manner that I am sure the bunnies do not take seriously, with his absurd ears flapping madly.
I am kind of thinking now that the bit of Brythen that is not greyhound is probably some sort of pointer. He has definitely been growing, and seems a bit more chunky now. His ears are very pointerish: when you see him with pointers, he does look rather like them (and he seems to get on with them particularly well - better than he gets on with a lot of lurchers, in fact, as lurchers often tend to want to play a bit rough for Big Soft Puppy). Plus, he points, one paw lifted, nose extended! Though I know that isn't necessarily a proof.
Thankfully, Az has been feeling a lot better recently, and has been able to walk much further and enjoy it too. Of course, this means he leads Brythen astray by setting off in a wobbly old run after OMG!Imaginary!bunnies!, or suddenly deciding to bounce and bark at a dog behind a gate. Disgraceful old hound he is.