I don't know where you get the idea that ANY type of sugar, including prime tabs would take LESS time than any other. The yeast won't eat one type any faster than another.
In fact one of the biggest complaints about prime tabs is that
it often takes LONGER for the yeast to break down the tablet as opposed to a priming solution.
There's tons of threads on here about folks complaining that it takes longer than they expect, many like you have some wrong idea that it would only take a few days, but also quite a few who understands the carbing process and how long it REALLY takes, and why, and they often say it takes longer than the
3 weeks @ 70 it takes.
Sorry, but there's really no shortcut to what is a natural process. The
3 weeks at 70 degrees, that we recommend is the
minimum time it takes for average gravity beers to carbonate and condition. Higher grav beers take longer.
Stouts and porters have taken me between 6 and 8 weeks to carb up..
I have a 1.090 Belgian strong that took three months to carb up.
And just because a beer is carbed doesn't mean it still doesn't taste like a$$ and need more time for the off flavors to condition out. You have green beer.
Temp and gravity are the two factors that contribute to the time it takes to carb beer. But if a beer's not ready yet, or seems low carbed, and you added the right amount of sugar to it, then it's not stalled,
it's just not time yet.
Everything you need to know about carbing and conditioning, can be found here
Of Patience and Bottle Conditioning. With emphasis on the word,
"patience."
Sugar is sugar, it still takes time for the yeast to eat it, then fart the co2 necessary for it to carb, and for the co2 to infuse the solution and the headspace.
Sorry to burst your bubble.