Moving the parents around is one of the fastest ways to get them to STOP breeding so in my experience with over 100s of pairs, it's best to move the eggs not the breeders or, see if the parent will raise the fry themselves.
Danios are not Angels and they don't spawn the same way so to compare the 2 is not really a good or fair comparison. Danios will breed in less than perfect conditions.
The better plants to use as spawning sites are the Amazon Sword plants due to their larger and thicker leaves. If you are not going to remove the eggs, those would be my plant of choice. Slate or tile or marble or clay pots all make good spawning sites and are easily removed. You just don't want to have a surface that is slick so the eggs can't attach to it.
Foot traffic is people or animals walking in front of the tank constantly. This can be upsetting to the breeders so they don't breed. This is why I put my breeders up high so that I can still walk through the isles and not disturb them. Once they get really used to your presence when spawning, they tend to not care. I've done water changes in the 2 tanks on either side to a spawning pair and they just kept on laying like I wasn't there. ( But I have also had fish stop and then eat their eggs so it's not a guarantee they won't mind.
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Hope this helps.