>>878265>>878266Carving hatchets are certainly a thing but, yeah, you put them down for detail work.
Another suggestion, if you didn't already do this, is to trace the top hole of the eye onto the end of the piece. This will give you a good idea of when to slow down.
Keep in mind, the fit of the head should be snug. You don't want it flopping around, nor should you need to beat tge snot out of it with a mallet to fit.
If you've sized the end properly, you should be able to hold the head in your hand and seat it fully with a few taps from w hammer on the bottom of your handle. The wood should stick out beyond the eye, which you can trim as desired after wedging.
You want you kerf to extend about 2/3 through the eye. Use a piece of scrap wood over your wedge so you can hammer it evenly (otherwise is breaks apart, which is fine but unsightly).
Your step wedges can be angled, but try to keep them inside the wooden wedge. Too much into the wood of the handle itself can cause splitting along the grain which can eventually extend down into the grip. Some people prefer to pound them in running perfectly parallel to the wooden wedge.
Obviously, choose the correct sized wedges for the application. One or two small step wedges will be plenty to lock your main wedge in place.