Articuno, Moltres and Zapdos could roam like in X snd Y, where they just autorun and you don't have a chance to throw a ball, and then end up on Ametrine, Pyrous, Shade's power plant respectively
In Red/Blue Rescue Team. In that game Mew was in a 99 floor dungeon and it would transform into other pokemon so you didn't know which one was Mew. So maybe you find it under a random train and then it roams while hidden as another Pokemon.
Regirock in a cave in the desert, Regice in Citrine or in a cave on Ametrine Mountain makes sense. Not sure where Registeel would go, maybe the depths of Tanzan?
In Emerald after you beat the game you could find caves/dive spots on random routes that were caused by Kyogre and Groudon. Whenever they were on a route there would be harsh sunlight/rain too. Maybe they find eachother and start fighting. That could lead to you having to find Rayquaza, who could maybe be on the summit of Charous Mountain, pretty sure it's the tallest in Reborn.
Uxie, Mespirit and Azelf I could see being in a quest related to Eve, Lumi, and Zero.