You should keep the rng for the skeleton keys how it is now.
But here's what we should do for those running a big amount of strikes in a row getting unlucky with the drops.
You get a gaurenteed skeleton key after 10 strikes. Heroic strikes and strikes from the siva playlist counts as 1 strike but nightfalls count as 2.
That honestly seems fair. 10 strikes is not too much and not too little. I mean I don't mind doing 5 nightfalls for a skeleton key. It's worth it cause the loot from those chests are usually higher than your gear by at least 3. Plus the artifacts are worth the grind. And for those who think 10 is too much it's really not considering you can level up from everything now. Archons forge. Raid. Trials. Three of coins. Even crucible.
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I like the idea of a surefire way to obtain keys Your idea would be good, im thinking however of a certain task or activity , like a bounty which you would complete each week for the guaranteed key