Using your measurement of 5/8" and assuming that the existing loft has
either no existing floor covering or the 5/8" represents the net
difference in thickness between the wood flooring and the existing
non-specified floor covering. I would consider pulling the carpeting
on the top several steps and adding progressively thicker layers of
masonite 1/8" on the fourth one down, 1/4" on the third, etc. You'd be
gradually increasing the height of several treads and the transition at
the top of the stairs would be less abrupt.

Simple to do, cheap, complies with code assuming the existing stairs
do, you should use longer fasteners for the tack strips, pay attention
to the nosings when you're installing the masonite. Make it so.

Actually, I don't think the gradual transition you describe DOES
comply with code. One of the numbers in the code is an upper
limit of the greatest allowable variation between ANY rises in
the stairway, it doesn't just apply to adjacent steps.

What OP needs is a landing at the top and bottom of the stairs
that has the same covering or lack thereof as the stairs,
and make the transition between the landing and the rest of the
floor, rather than between the landing and the steps.