I've had to change flywheels twice in the last 12 months.
The first was because a car had a counter-balanced weight flywheel when it shouldn't have had, and you should have seen that engine trying to climb out of the car!
The second was due to a clicking noise caused by a cracked flex plate.
For the first one I simply machined off the counter weight and, since the engine was in bits, had the whole crank/flywheel/clutch/damper assembly balanced as a unit by these excellent people:
http://www.vibrationfree.co.uk/The second left me in a bit of a quandry; I could simply order a new flywheel to part number at £350 but I had no guarentee that the engine or crank in the car were the original items. I was therefore concerned that if I ordered the "correct" part it wouldn't actually fit when it arrived. I decided that I would be better of finding a second hand flywheel that matched the failed one.
The combinations of hole size and counterbalance were then revealed with two different bolt hole sizes being found on both types of flywheel. I couldn't find a satisfactory flywheel without the counterbalance so I asked the same people above to modify and balance a counterbalanced one to suit my requirements.
A little long winded but it was the only way I could guarantee results.