"synchro balanced" would indeed indicate something like a
briggs 320424 (14hp)
maybe 325431 (15hp) or something..
but it surely looks like such cast iron mostrosity of an engine
And I recall seeing Briggs and Stratton with 5 stamped lines (this orientation for horizontal) and "downward" for vertical shaft engines...
I just can't put my finger on a year to narrow it down I'm afraid..
a quick google yielded this however:
https://www.ebay.com/itm/Vintage-Briggs-Stratton-Blower-Housing-Shroud-10-HP-/142690476163
see? lines!
'sid
PS looking at older cast iron briggs in the 10-15hp range I'm rather confident it IS a Briggs&Stratton engine,
that cylinder casting with the "seperated" exhaust fins ... really similar to what you got.