Thunderhead has major conception issues as everybody seems to agree. A dot tied to a buff which has the exact same duration is really bad design as someone already mentioned in another topic, that and its underwhelming potency on proc which makes it all the more important not to clip it make thunderhead one of the main issues and hindrances to what used to be a smooth BLM gameplay experience. Keeping the uptime of a dot is always something that jobs have to work around but High thunder might be the clunkiest out of all of them (why can't we just cast it whenever we want anyway?).
So yeah increasing the duration of the buff would be more than welcome (still can't wrap my head around why they reduced proc damage to increase dot damage in 7.05 but oh well...)

As for Flare Star... so much wasted potential imo. The idea of being able to cast it with fewer stacks while more stacks lead to more potency has been going around for a while and would honestly be much better design for the skill. I'm personally a bit pessimistic and highly doubt they would ever go as far as grant us this wish.
I personally think that making it instant would be a decent change, although as you said it'd take away from BLM's identity as a turret caster even more... Yet another 3s cast on top of Despair was not necessarily something that we needed, I don't think BLM's rotation needs an array of finishers like RDM has.
If we are to keep it as a 3s cast, then PLEASE make it feel impactful. The skill dictates our entire rotation and gameplay, it's what prevents us from having more flexibility so playing entirely around a skill that has 160 potency less than Xenoglossy is kinda meh... It's supposed to be our finisher, we have no guaranteed crit/dh (not that I advocate for this) at least give us some screen shake I beg you.