I would get that release word working right away. It is important that he regularly hears this release word just prior to getting up or breaking the stay. It's part and parcel of the deal. Break your stay down into three parts; duration, distance and distractions. When you're working on one part or criteria, relax the others. For instance, start out with durataion. No distance and no distractions. Go in a boring room and stand right smack in front of him. Have him sit for just a second, click/treat, release quickly. Get that release word in double quick before he screws it up. LOL....before he gets a chance to rise or break the stay. He'll get so it's habit for him to have getting up from the stay preceeded by the release word. It will help him learn to wait for the release word.
Don't start using your verbal cue until he's getting this pretty regular. Just get the behavior. (even if he has learned it before. If he's not so good at it, you're liable to louse up the cue) So, save it till he's really getting onto the game so he doesn't miss the association between the cue and the behavior.
Work on your duration gradually, only increasing it as he succeeds. Then work on distance and relax the duration. Step back a step and immediately return to him. Then two steps back and immediately return. When you come back to him, click/treat and release. Gradually add to the distance. If you forget to use your release word or don't get it in there quick enough and he breaks the stay, he just lost an opportunity for reinforcement. No punishment. Just start over.
Then when he's getting onto that, you can then add the two together, starting out on easy street and gradually adding pressure.... or you can throw in some mild distractions and stay with duration or distance training only. It doesn't much matter what order you do it in, just as long as you make it easy for him to build reinforceable responses. So, if you decide to throw in some distractions, it's best to relax the other criteria (distance from you...and duration of the stay)for a bit.
The click comes at the end of the behavior. So, as you build duration very gradually, you'll be clicking at the end of your pre-determined number of seconds. As he gets pretty decent at this stay business, you can start clicking NOT when you're right in front of him, but from a distance and rush in and give him the treat. You will want to mix things up so that stay doesn't just mean stay because you're standing right in front of him. You'll want to turn sideways, stand in different positions from what you usually do. You can sit in a chair and ask for a stay. You can squat and ask for a stay. Have him vary HIS positions too...sometimes lying down and staying, sitting, standing. Stop when you're just walking around the yard and ask quickly for a stay right where he is. Mix things up so the stay gets on stimulus control. Try to gradually start standing a little differently asap because once he gets it in his mind that you're always, always standing a certain way, that becomes part of the cue and you don't want that. You want stay to be singled out from everything else so it will mean stay no matter what else is going on.
But imo, the sequence should be: Correct response (make it VERY easy to comply), click, treat and release. (gradually raise the part of the stay you're working on and then add the criteria together)Try to avoid exciteable wild praise, as this is likely to make him break the stay before you've gotten your release word in. You can save that for later. The click and treat is sufficient reinforcer.