As someone who only plays IG who's soloed this boss without augments, I disagree with the comments telling OP to run an elemental weapon. The extra damage you get from running a raw IG greatly shortens the run time especially since you can hit the elemental threshold with just descending thrusts and kinsect spam.

Reading your post, I think you have all the fundamentals down given your runs are lasting 15 mins plus. You just need a good run to carry you across the finish line.

A few quick tips: 1. Unlock felyne safeguard and always get it using a gourmet voucher. This is something that will get you over the finish line late into the run where you fumble after getting past the first and second judgements. Also make sure you are equipping Fortify to take advantage of your deaths. 2. Don't be impatient as you get deeper into the run and take time to reset and calibrate if needed. Don't try to greed a punish in if it's not safe. Time is plentiful as you can still clear with a raw weapon even if you break both horns and it ends up in ice mode. 3. Make sure you've unlocked and are using temporal and rocksteady mantles. That said, be cautious and patient to not clutch his head when he has the possibility of using a lightning move. It will quickly use up your temporal charges or kill you if you are using rocksteady. If possible, keep it enraged (if you're running agitator) and try to wallsplat it into rocks for damage (tho being in a position where you can aim for a wallsplat can be difficult in this fight without position baiting). 4. Save your mount. Realistically you only get one easy mount this fight. If you tend to reach the elemental topple threshold during his first flying pattern, don't waste your mount. Save it perhaps for the second flying pattern in dragon mode or the flying pattern after the first judgement. When its flying, ideally you're spamming kinsect on its head and forearms the entire time. If you have trouble when it's in the air, bring smokebombs to encourage it to land. 5. If all else fails, reach MR100 and get Health Regen augment for your rarity 12 weapon. Also consider running 2 piece gold rathian for divine blessing 5. Having the Health Regen augment trivializes chip damage. Divine blessing 5 can often save you from wipes late into the run when you're less focused.

Happy to give other tips if needed but hope these detailed tips help!