PG, I think it would be cheaper and easier to scrounge a more or less junked engine, or parts to repair your old one. A lot of those Briggs parts you need are as close as your nearest nature strip. However you will have a problem with the crankshaft - the 9 cubic inch engines used in vertical-spindle mowers have seven-eighths inch output shafts.
I don't know whether the 9 cubic inch engine has the same stroke as the 8 cubic inch with a smaller bore, or the same bore with a smaller stroke. If the stroke is the same you could get your machinist to turn down the output shaft of the crankshaft to five-eighths, but cutting a new keyway would be a bit of a pain (it's a milling job).
My preferred solution would be to find a more-or-less unwanted, horizontal crankshaft Briggs, Honda or Tecumseh that will physically fit your mower. I wouldn't care whether it was 6, 8 or 9 cubic inch displacement, so long as it was easily fixable and it fitted (which I suspect most of them will, except for the output shaft diameter of the 9 cubic inch engines). Unless you are unlucky, you should be able to get such an engine for less than $50 (possibly a lot less) if you don't mind replacing the rings and lapping the valves yourself.