I think your estimate is at least 50% too high because I have bicycled 50 miles before and it wasn't exactly strenuous.
6300 kcal is ~19 million foot pounds, or you would need to stair master 97,300 feet.
Assuming that you can stair master at 10% efficiency, you would need to do the equivalent of climbing ~10,000 feet. Most people can do better than 10% efficiency especially bicycling, so adjust accordingly.
One way to measure how much you actually burned is to bicycle up a grade that duplicates what feels right, or find a grade you can coast down at the same average speed you traveled at, then do the math to find the work done. Compensating for the elevation gain/loss is easy but the cubic function of wind drag complicates the matter for steeper grades.
The most I've burned in one day was probably hiking up a mountain for 4000 feet gain and back down in one day, I was 150# at the time carrying about 40#. Most burned in 4 days would be a 4 day loop around a mountain, gain and loss of ~26 Kfeet in just 45 miles, I carried about 12 pounds of food in and still lost weight, i don't even recall taking a dump in those 4 days.
I've maintained 1000cal/hour as per the machines at the gym, but I can only keep that up for say 10 minutes and my heart rate will be around ~180. Last year I could keep my heart rate above 160 for an hour on the same machines burning about 500cal/hr, and my resting heart rate was below 50.
fat has about the same energy density as gasoline btw, it takes a LOT of work to get rid of it.