I'm trying to think if you could custom build a custom nose piece, it could be applied to the face of the tread. I'm thinking like a 1 1/4 inch tall piece of oak 3/8 of an inch wide, steam bend it to that radius. You'd have to be careful but if you applied that trim piece so that it extended 1/4 inch above the tread surface, you could then make a pattern and flush fit the LVP to that edge.
I bought a Powerball ticket tonight. If I win, I'm going to build a shop and put a steam bending chamber in it. Maybe then, I'll do that set of stairs for free just because I'm a nice guy.

Now if I don't win, then they're not gettin' any stairs.
I suppose a guy could make a pattern of the stair out of 3/4 inch plywood, then heat up a piece of flat steel red hot, then bend it around the pattern and you'd end up with a 1/4" steel edge which you could screw to the existing nose.
You could have the metal polished and blued or powder coated........
Oh my goodness the possibilities are endless.

It's been a long week I should probably take a nap

I sure wish I had a shop and a bunch of tools that I don't have. It would be kind of fun tinkering around with ideas and see what could be handmade in a situation like this. I know if you had somebody build it it would be outrageously expensive.