First of all, I will just say that it wasn’t string. It wasn’t string, because if it had been string, we would’ve seen Sherlock playing cat’s cradle instead of bouncing a ball. (Though if someone wants to draw Sherlock playing cat’s cradle that would be awesome because now I have that mental image stuck in my head.)
As for the rest, I think we have completely different ideas of how the rubber ball trick worked? Here’s how I currently imagine it happened:
1) Sherlock fell from the building. He flailed his arms around, so I think we’re pretty safe in assuming he wasn’t trying to do the rubber ball trick on the way down or anything (not that there’d be a point to that). The ball was tucked safely in a coat pocket or somesuch. (Possibly it was secured safely into his coat sleeve considering the weird way he moved his arms at one point on the roof, but I don’t think that’s going to be provable to everyone’s satisfaction just yet.)
2) Sherlock came down, something broke his fall, and he ended up landing basically face-first on the sidewalk. He bounced a little, but not really enough to explain the next position we saw him in. But that’s okay, because there’s no real mystery there— he was still alive, so we know he was able to adjust himself to whatever position he wanted before the truck blocking sight of him pulled away.
3) And that position was the one seen above. He took the rubber ball, jammed it in his right armpit, and then intentionally chose to lie like that, putting as much body weight as he could into pressing on the ball and cutting off the circulation in his outstretched right arm. (And do note this was the position he chose, as he was in it before anyone came along and began fake first aid.)
4) You’re right that his pulse would reappear as soon as the ball was removed, but it wasn’t removed. Sherlock lay still like that, pressing the ball in place until John could come over for his scheduled pulse-reading appointment.
5) John got his chance to check the pulse. Sherlock’s hand was a little blue by then, so he must have seriously been cutting off the circulation. They may have exaggerated the color a bit so it was more of a clue for us later, but all of the instructions I have seen for the pulse-stop trick do point out that you really shouldn’t do it for very long at all or you will mess yourself up. I don’t currently feel like testing how long it takes my own hand to get that blue.
6) Only after John had been allowed his one-and-only chance to check the pulse did they move Sherlock’s body at all and therefore risk dislodging the ball and allowing his pulse to return. And of course it didn’t matter if his pulse did come back then, because from that point it was all a big body-switching coverup anyway. The entire pulse thing was 100% for John’s benefit.
And this has nothing to do with the asker’s question, but while I’m on the subject of the pulse trick… I’ve seen some people point out that it didn’t matter anyway, because you can’t always get a pulse right away and John didn’t have a fair chance at it. But John is 100% a pulse-checking kind of guy (I’m serious, go back to Scandal), so Sherlock was going to have his bases covered. The “death” would be more convincing for John if he was allowed to at least attempt a pulse-check, but the last thing Sherlock needed was for something to accidentally go right for John that day and him to successfully detect a pulse in the brief time he was allowed. (What if the older woman holding him back hadn’t been able to pry his hand off of Sherlock’s wrist as quickly as planned? You can’t assume that would go perfectly.) So he used the rubber ball trick and forced John to check the correct arm to make sure that wasn’t an issue.
I didn’t come up with the rubber ball pulse stop theory, but there’s a lot of evidence for it. If I had to choose one thing to bet money on for being part of the actual solution, right now it’s probably what I’d pick.
And considering the word verification check I just got while uploading the images for this post, I think maybe the universe agrees with me: