Rather than getting the correct screws, if you MUST increase the CS size on your piano hinge I'd suggest using a centre drill (otherwise known as a Slocombe - presumably a Mr. Slocombe invented them, dunno).
If you're not familiar, image a VERY short twist drill with a normal drill point at EACH end, separated by a centre body with a much larger diameter than the drill part. They come in sizes which are numbered and there is a defined relationship between the diameter of drill part and the centre body. You'll have to try different numbers to get a drill part which suits your hinge (without enlarging the hole itself) but which will give you a bigger countersink without encroaching too much on the hinge line itself (or on the edge of the strip) - holes bored into piano hinges that are too big and spill out over the edge of the strip (or graunching onto the hinge barrel itself) are not only structurally unsound but also look horrid!
You can find the diameter/number details out by consulting the online table available at (amongst others), Arc Eurotrade, whose details are on the sticky at the top of this General Metal Working section.
The reason why I suggest a Slocombe is that being very short but with a thick centre body they are very rigid (their basic purpose is to bore centre "pips" into bars, etc on the lathe). They are also VERY sharp which is ideal for SS.
If you go this route, be careful of SS work hardening while drilling and countersinking, as said above. To overcome this you need a rigid countersink bit to prevent chatter, VERY sharp, slow speed, quite heavy feed - ALL of which suggest the Slocombe (although that's not its original purpose), plus LOTS of coolant. If you need to stop machining before you've finished countersinking be sure to allow the job to cool before starting again, and as above, expect the job to be even tougher than first time. But take it carefully as above and it IS doable. At a pinch you could try this in a hand-held drill, but a pillar drill is by far and away the best solution.
But as already said above, an even better solution is to get the correct size screws - it's VERY easy to ruin a piano hinge by graunching the hinge barrel or running off the edge of the strip!
HTH
