1) Make it possible to trigger more plot-related dialogues on each rest (for each companion). The problem with this solution is that the first dialogue could end with an irritate companion and the next one with a perfectly amicable one, depending on the trigger conditions, without the passing of in-game time to justify the change in mood.
1.) I'm assuming be "for each companions" you mean "
maximum one dialogue per companion per rest"? This eliminates the possibility that the same companion has 2+ dialogues in a row, one where they're irate and then another where they're happy.
2) Trigger the conversation right after the condition for the dialogue has been met. This solution can slow the pace of the game but at least it will be coherent.
I don't think companion conversations should happen automatically. The player should be required to do something to initiate it; e.g., clicking on the companion or even short resting.
3.) Some camp dialogues - any that don't require sleeping - could occur during short rests or out in the overworld. This could coincide with actual short rest mechanisms, where you choose how many hit dice to spend, and making short rests feel more impactful than a single click of a button. If Larian really needs the background to be the main campsite (because that's where they rendered all the camp cutscenes), I'd be okay with the game bringing you to a camp-like area (basically the usual camp area, but without any tents/npcs/etc) for the short rest. This would multiply the amount of opportunities for companion dialogues by 3: 2 short rests + 1 long rest per day.
As for the ticking clock of the tadpoles, the best idea I could think of was making every long rest equivalent to a [illithid] dialogue use, so everytime you rest the stronger it grows, you'd even start having the dreams with every long rest.
I like this. Currently, the game doesn't have enough tension. There is a tadpole in our heads; we should feel some urgency! Even if we aren't immediately transforming, there still is a chance that at some point they will be 'activated' and instantly turn us. Although the frequency should maybe be reduced: every 2-3 rests should be equivalent to an [illithid] dialogue use, not every single rest.
If this is implemented, there would need to be a dedicated cutscene where it is spelled out that resting will slowly make us more in-tune with the tadpole.