...how much it works in particually off-putting/deadly arrival areas, I don't know, but I choose to craft-craft-craft whatever mundane stone I have the most of (and the least use for, myself) and that glut of goods (perhaps needing the Caravans to be able to happily take them away? - another problem your chice of embark zone might interfere with, drastically) quickly draws the immigrants in. An embarassment of arrivals, in fact.
So maybe you just need to make loads of whatever goods you have a penchent and ability to make.
But, in dodgy biomes, I also try to ensure I have sally-ports set up at each corner and mid-edge of the playing area, ready to disgorge military (rarely necessary) or attract migrants arriving anywhere but where the enemy is currently prowling (and with leverable bridge-walls, up to the very edge, I can often ensure western-edge siegers can't interefere with eastern/southern/northern-edge friendlies of all kinds, or even isolate to the octant level of perimeter restriction!)
Not that it necessarily helps if you're trying to please a dead/dying home civ, as noted. And, by now, my play philosophy might be a bit more out of date.
(I already try to switch from (say) mugs to (e.g.) scepters before I get the idea that the traders are going "Oh no, not mugs again!", behind my back. And I know this was a definite future design aim by Tarn, at one point, to discourag flooding the outside world's marketplaces with such tat...)