Which overhauled Lycoming 0-360 A4M Engine To Fit In My Archer ?

Do you have a mechanic to work with who will sign off a field
rebuild...
You might consider sending the case, crank, cam, con rods, to Divco for
IRAN and balancing (or Aircraft Specialities, etc.) along with the new
cylinders of your choice of brand... Press new bushings in the rocker
arms... Send the carb, alternator, vac pump, oil pump, for overhaul...
Overhaul the mags and install with new wires and new hoses... Then
with your mechanic put it back together... This should be less than
the highest bid you had for an overhaul and will give you the
equivalent of a new engine...

denny