with the saw together with plug with starter off, can you rotate flywheel with ur fingers and will turn over? (will be hard but not difficult)
if yes, then ur starter may be issue. did you put knot at pulley end or did u use noose type were rope wraps around pulley will no knot? if knot, then knot may be binding against flywheel as there is no clearance for knot on old some HQ starters (but 272 should have deeper pulley shaft?
they also used different pulley shaft lengths for various series of starters (all same engine family) and could be hitting flywheel-
if you put starter mounting screws on loose-barely holding starter on-is it still tight? also you never did check pulley for warp or cracked on inside from what i read- as it will bind starter and give a false feeling that it is engine
sometimes its the simplest reason