You may also want to try grinding the tang area of your tap to reduce the over all leangth,just grind the new area for your tap wrench(the square section)before you shorten it.The tang area does not have to be as hard as the tap end,so lacking a grinder you can soften it with a kitchen stove,and have at it with files.To keep the heat from migrating to the cutting teeth,clamp a pair of brass or copper blocks above the area you wish to remain hardened.
To reduce the oal on the lead(tappered are at the beginning of the tap) a Dremel tool or a bench grinder can be used to trim it back,but continually dip the tool into cold water to retain the temper(hint:if its too hot to hold,its getting too hot).Just make sure you grint the lead end evenly.
hope this was some help,N.L.Byiers