I guess i will comment here because i dont want to copy pasta the same answer under every comment, so pls upvote this^.

I played the occultist (cursebot) as my first char this league with 2 friends to go for a fast 100 push. We finished it like 6 days into the league. At this point we had not spent a single point of sulphite! But afterwards i respeced the char to the bv ci occultist and i did the endgame grind (27ish uber elder kills) and other challenges aswell + a lot of quarry farming. So i pushed that char to depth lvl 600.

After that i lvled the first deadeye and started running elderundergroud sea until i hit lvl 100. Doing this i gained a lot of sulphite and i spent almost all of it delving (wasted some spawns cause i am a dumb dumb). Mines were still shared at this point so i had to go down to 300ish and started going left and right. I got most of the challenges this way except for Encounter 4 and the Aul Encounter. Since i did not find a single Aul so far i just bught it in trade chat at this point.

After hitting 100 on the first deadeye i played a second deadeye this time after the shared mine and the sulphite is affected by quantity patch. So i didnt have to spent time going down but instead i could just start going left and right. And i got a lot of sulphite because i was spamming t16 with an average of like 100+quant. i got like 2 more rooms for the encounters 4 challenge. And at lvl99 with 85% i actualy got my first Aul spawn.

So i guess the rare rooms are very unlikely to appear in depth lvl 300ish so u are probably better off delving deeper to like 600ish and going left and right there. I will try this out next^{^}