If it were me with the distance work I would work on her understanding that you don't have to say stay but rather that she holds whatever position until given a release or another command. I don't teach a "stay" but rather work really hard at them understanding that if I saw sit they stay sitting until I tell them to do something else.
I would work on that until her commands were solid and she won't break and then start adding a little bit of distance. If you don't think she's going to stay and down when you're two feet away just do one foot and slowly increase it.
If at all possible I prefer to avoid using props that I will later have to fade out, just my personal preference. For down in motion instead of starting it on the recall I started telling Traveler down randomly and suddenly (during actual training but also throughout the day or on walks. Did the same with stands and sits also). We would be walking and I would just say "Traveler DOWN".
At first you might have to sorta of body block and have more exaggerated hand motions for the command because they aren't used to it. But that really seemed to get Traveler to understand that a command could come at any time and used to obeying before he thought about it. Then I started running around with him next to me and giving him the command while he was moving faster to slowly fade out the run, slow down and then lay down response a lot of dogs seem to have with the down on recall. Wanted him used to downing while running and it's easier to reward and shape when they are next to you rather five feet away running at you.
Also, avoid slippery surfaces when you start out, they don't seem like they like going down fast on rhose
Here's a little video that might give you a tiny bit better idea of what I'm talking about. This was months ago but we had been doing the random command thing for a little while so he was pretty good at it. Do not use it as an example for what I said about each command not being broken until released :rofl1: I was terrible.
YouTube - Positions‏
I think really working on the dog understanding the command at it's whole rather than it being situational would help in both of those a ton. When I'm training I lay on the ground and give positions, I stand on a table, I turn around and face away, from behind them etc. I want the dog to know that no matter what I'm doing the command still means do that behavior from where ever you are. I really think doing that makes them understand better than it being "Down is the command I do when she's standing in front of me looking at me" and they start get that it's what they are doing and not so much dependent on how you are positioned too.
Just the other day I saw how it's all kinda paid off with Traveler. I was working with him in the front yard and forgot something inside so I started to leave and he was following me so I just said without looking behind me or using any kind of hand motion to down. And he hit the ground. Didn't matter I was walking away, down means down.
Not sure if any of this made sense and kinda turned into a ramble. Sorry!