Josh - assuming that you will strip-off all the old varnish/paint using mechanical, as well as chemical means, what you are left with is the carpentry solutions.
Assuming the tread surfaces are only slightly worn (difficult to tell from the photos) then the least disruptive method of repair is to cut off the nosings flush to the risers - a router then finish the corners with a handsaw. Attach new nosings with biscuit joints and glue.
If the tread surfaces are too far gone, then replace as in your option 2. However, in the UK this wouldn't be possible 'cos of the regulations (all risers have to be the same height and the top one wouldn't be); maybe in the States your codes don't cover this so you could 'get away with it'.