You have a strong profile, but unfortunately yes--luck seems to play an immensely large role even when it comes to top 1% candidates. I have multiple anecdotes of friends or acquaintances who ended up with 4+ VS's and TC offers at absolute top of the market firms (Kirkland,
Latham,
Davis Polk, W&C, All the MC, etc.) getting 10-20 rejections from 'less competitive' shops.
Application quality also seems hit or miss, had one friend who was a megafan of HSF; attended 3 Open Days/Events, came top in a HSF sponsored negotiations competition, spoke to grad rec, spent ages crafting the best possible app, got trainees and alumni to review (with great feedback), passed the SJT.
Rejected at the first review stage.
By contrast, that same person made an application to Milbank on a whim, barely submitting minutes before the deadline. Spent probably less than an hour on the application. Eventually got the TC there (and at 3 other super tier US/MC firms most would consider more competitive than HSF).
Same guy also got rejected from other US/MC firms, large national firms, SC firms, etc.
Persevere.