Your need is common for "field dogs: as well as avalanche rescue dogs.
The "games" you are playing serve the purpose, as you are always in the activity. Hand commands and other physical triggers are GREAT! Dogs are so tuned in.
But what if you wanted your dog to stay while you went to lunch. Say an hour or maybe two. Start by just going out of sight. If the dog breaks, return it to the spot and try again. NO REWARDS, maybe a Scowl. be indifferent during the relocation!
You need to structure the command to the expectation.
Hmmmm.....OK. I'll work on extended stay when I am out of sight.
There is no reason that a hand "down" can not hold a TEMPORARY stay of activity.
Use a hand UP for a follow up. With a "STAY" command requiring a higher level of permanence.
I celebrate you for working hand signals! Keep that dog paying attention to YOU! You both will be happier!
ETA
Why would you require the dog to "come" when all you wanted was to release it from the "stay" command?
When she finds or retrieves the ball/toy I say Wait.....she will stand and look at me and usually drop the ball.... I will have her sit....sometimes sit, then down....depends. I say Ball and Come. She'll p/u the
ball and bee line to me. I say Come because I want her to return the dang ball! I think she's learning, we're
burning off a lot of energy and it's fun for both of us. I'm not trying to raise a avalanche rescue dog (live in Tx...not too many avalanches here).
I've also been using 2 balls. Sometimes throwing 2 out in different areas. She'll get both, but can only fit 1 at a time in her mouth. So I use Ball and Come and she will bring 1 back. Then send her for Ball #2.
Working with dogs suggests "computer language"
Explicit, distinct, and format matters!
eta...
I once had a friend that issued a "CHARGE" command when he was meeting another person and wanted his dog to lie down and be unobtrusive.
Sure got the other person's attention! ;-)
As a side note: I took her to HD with me today. She is not over friendly but not aggressive. Not interested in most folks, just the noise and unusual sounds/activities. However, there was a guy in a wheel chair there
and she got really close to me when he went by. I waited a few seconds and then asked him if it was ok if I brought my dog over to him. He was very gracious and said sure, then slowly lowered his hand. She gave his hand a good sniff and just sat down next to me. Seems like a small thing, but for her to even approach
someone to give them a sniff is a big deal. She will refuse dog treats from workers at HD or my dry cleaners and TSC. But if they give the treat to me (and no, I didn't eat it myself) then I give it to her she'll eat it right down. (I'm ok with this because I really don't want strangers feeding my dog. Am I a bad Dad?)
She just turned 1 yr old. She goes to work on the farm with me and just hangs out or explores when I'm fencing etc. I love this dog.
