Good job on the paint work, the red looks like a vermillion and the white passes for lead white.
I hope you have nice thick brush strokes like the surviving ones.
" I was told that the original egg tempera paint would have given the helmets a gloss finish"
You mean a matte finish
You don't want to paint a sallet with egg medium in any case, egg is painting for wood and cloth.
As you have used a gloss paint you don't need any more varnish as the gloss medium is varnish and it will of course be waterproof.
I have just received a kettle hat which I will be daubing on, yay.
Remember paint was cheap, painted sallets/helmets etc that survive are often the less expensive sort, paint was used to buff up inferior work, so the odd ding is ok