I'm getting back to woodworking after many years away from it.

I'm trying to plane some birch that has a knot close to the side resulting in some irregular grain.
I'm using a Stanley #5 plane that is about 40 years old.
I'm using Norton stones - 1000, 4000, 8000 to sharpen the plane iron.
I'm able to get the blade fairly sharp. Sharp enough to cut some of the hairs on my arm.
I remember from years ago, that when I would sharpen my Marples chisels I could get them sharp enough to cut every hair it passed over on my arm not just some.

So with my plane iron as sharp as I can get it I am still getting tear out on the board I am trying to plane.
I'm wondering if the alloy in the plane iron is not allowing me to get it sharp enough to minimize the tear out.
Can anyone tell me if I am likely to get significantly better results with a new Veritas PM-V11 bevel up plane than my 40 year old Stanley?

My other option is to buy a PM-V11 iron for my Stanley plane but the cost of this is about 1/3 the cost of a new plane.
From what I see on the internet a bevel up plane will give me more options to deal with irregular grain so a new bevel up plane seems to be worth the additional expense. This of course is based on internet info so I am interested in getting other opinions based on experience planing boards with irregular grain.