Adding more sugar doesn't imact the speed of carbonaton as much as it impacts the final amount of carbonation. The yeast will eat every bit of the available sugar, whcih gets converted to CO2.
I'm assuming that you bottled five gallons of beer. Do you happen to know what the highest temperature that your beer reached?
It's hard for me to guess exactly how much sugar you got from the juice of "about 3 oranges", since you didn't tell us the volume of the juice you added. Also, measuring sugar by volume (a cup) rather than weight (8 ounces for sure) adds uncertainty... you can pack sugar in pretty tight, if you try.
That being said, you absolutely overprimed. Three volumes of CO2 is a pretty fizzy hefe... by my best guess, you are somewhere around 4.2 volumes or so. If you came up shy of five gallons, if the beer was kept fairly cool, if you added more juice... you could be looking at 4.6 volumes or more.
Most bottles are only good for 3.5-4 volumes of CO2. Above that, and you run serious risk of explosions (aka bottle bombs). Not only did you potentially waste the entrie batch, but this is VERY dangerous.
If I were you, I'd open every lid after a week in bottles. This will vent the CO2 that has been produced. Then go on and re-cap them.
As high as you have carbed, you may even want to repeat this process after a second week in bottles.
If you just leave them as is, you have very little chance of getting drinkable beer.
Next time, use a tried and true rule of thumb - an ounce of sugar per gallon is good for most beers if you aren't trying to carb to style. If you want to be precise, use a priming sugar calculator like the one iin my signature.