I have one extra wheel which is unmounted and is 4.00 x 16, six lug. I measured the hole and it is 5/8. This wheel is for both my '42 and '51, so I assume it is the same as yours. It had a tubeless type valve stem in it which I removed to measure. Possibly someone drilled it out? It is definitely 5/8, not 3/8 or 1/2. Maybe someone else can offer advice.
Kent