Agree. After sawing off the old nosing, I'd probably get a really thin 1/4" (or less) sheet of nice plywood and glue/nail it to the riser of that top step before putting on your new bullnose. This will hide that ugly horizontal line left when you cut that nosing. Use something like polyurethane construction adhesive to stick it on, then use latex caulk around the sides and bottom to hide the gap.