By being very quiet? The skill is called Stealth, after all, not Hide in Shadows.
The rule for blindsight, which you quoted, doesn't say anything about perceiving "as though seeing", or "like sight", or "as well as sight". It just says the creature perceives "without relying on sight". In many cases, blindsight is desribed as being due to enhanced hearing, in which case it could be defeated by being sufficiently quiet, or behind a wall. It depends on how the DM rules it, but it doesn't automatically negate stealth.
Not that the rogue being able to hide would've made a lot of difference in this encounter. Sounds like most of the PCs were basically doomed as soon as they stepped into the dragon's lair.
There is no vague meaning. Perceive means detect. Blindsight does not say "detect location", but perceive surroundings as in everything. Stealth doesn't work against them within the range. It's not a vague rule. Not sure why anyone is trying to make it one. There is no Blindsense and Blindsight now.
You can stealth on someone with truesight. But not Blindsight. Nowhere does it say perceives with hearing. So moving silently is irrelevant.
At this point in time barring any clarification from the developers, if you are within a dragons Blindsight range it knows you're there whether Stealthing, invisible, or what not. It's not even something open for discussion unless you're somehow arguing the meaning of the word perceive.