Looks like she's leaking a fair amount of fuel around the linkage there.

I did this recently. I found a core on ebay (Holley 847, same engine as you) and sent it down to John Plaskan in Florida (I can provide his contact info if you need it), and had it rebuilt for modern fuel (ethanol) for $225. Not cheap, but the thing looks brand new and was literally plug & play on my Flathead 6.