I am installing 3/4" hardwood 2.25 inches wide over an existing stair tread--just the top stair tread. I previously had carpet laid over this tread. The edge of the tread is rounded.

I was going to complete the installation by:
1--cutting the rounded portion of the stair edge off
2--installing a stair nose over the end where the rounded portion was.

the step height goes from 8" to 9" when I do this because of the thickness of the underlayment and the hardwood.

What have you done or what would you do?

Thanks

Remove and replace tread.