Daft question: can a 1/2" spacer be added between the chuck halves to get the extra amount required for 5C once the nose taper is re-ground??
Like I said, daft question, but assuming it can be split, that raised the question in my mind whether that was a potential option.
Perhaps an adapter collar to take up the 1/2" and a 1J angle on the outside to fit the chuck and a 5C angle on the inside to hold the collets.
No need to modify either one. IF you can make it work.
My thought about modifying the collets was that 5C are much more readily available and "converting" some to 1J would preserve the chuck and only risk the loss of a single collet.