Should I factor the blind schedule speed into my range?

So I'm aware that a lot of players adopt the strategy of increasing/decreasing their range based on how many BBs they have. Deeper stack means less urgency, and plenty of time to wait for premium hands; small stack pressures you to play marginal hands because you can't afford to wait any longer before making a play. I know not everyone plays this way, but this question is directed specifically toward optimizing this strategy.

Should I consider how fast the blinds are increasing when I play this way? Does 100 BB at a table with 12 minute blinds call for the same range as a table with 5 minute blinds? What about 30 BB?

I don't think it should make a huge difference, you might play marginally looser with the shorter time of blinds. In either situation, once you get to 10BB or less, it's pretty much shove or fold.

Widening your range based on blind levels

I'm a firm believer that players should widen their range when dealing with a small number of hands per blind increase ratio. I word it that way because playing live with 15 minute blinds will give you a lot less hands than playing online with 15 minute blinds.

But another thing to take into consideration is how quickly the blinds level. If blinds level 500/1000 then 600/1200 then 650/1300 you should play tighter than if they level as 500/1000 the 750/1500 then 1000/2000.

Blinding out is one of the worst things you can do, and if you're not paying attention to the speed or blind level increases than you're only setting yourself up to be in a shove/fold situation.

I have played lots of freerolls with different blind structures and it becomes crystal clear after a while that the faster they grow, the wider your range has to be. That's why I really don't like Hyper Turbo tournaments. You have to get lucky very often to stay in the game. It's virtually impossible to grow your stack steadily. You'll have to shove way more frequently than usual just to stay with more than 20 BBs.

Longer blind levels reward skilled players. You can make sound decisions and take calculated risks to grow your stack and, if you manage to win a few good hands every now and then, you'll be above average most of the time.