We started by marking and...
We started by marking and cutting the original raised portion hood ornament perch out of the hood.
The blue paint is layout die, which is marked with a scribe. There was no need to be careful here; the hole will be cut wider later to accommodate the new peaked panel.
The hood of a '55 Chevy somewhat resembles a huge tarmac, so it's not surprising that the design team at GM bolted a gigantic chrome plane to it. Fifty years later, it seems almost sacrilegious to alter a stock-bodied Tri-Five Chevy, but the hood ornament has to go if you want to build a hot rod or custom '55 (the latter of which there are far too few examples).
There are two ways to finish the peak on a hood: You can shrink the existing ornament mount to match the rest of the peak, or you can cut out the existing nose, fabricate a new one, and weld it in. We're going with the latter method, which, although rather difficult, is easier for the less skilled metalworker.
The major drawback to welding in a new piece is the warping caused by the shrinking effects of welding. The sheetmetal in these hoods is rather thin and flimsy, so it moves quite a bit when it shrinks. With a lot of patience (or a lot of Bondo, whichever you prefer), any amount of shrinking can be remedied, and I think making a new peak is more accurate than shrinking the existing metal, although that is up to the builder's discretion.

We cut a piece of sheetmetal...

We cut a piece of sheetmetal large enough that it will overlap the cutout by at least an inch on each side. Always make sure the new metal is of the same gauge as the original sheetmetal.

A buck helps to recreate the...

A buck helps to recreate the exact radii of the original hood peak. This one was made from a 4x6 block of wood.

We cut a V into the middle...

We cut a V into the middle of the block and then ground a radius into each side with a sander (a file will work as well). The radius was checked several times, as we were working it by placing the block over the original peak on the hood.