Sorry you're having problems.
I'm surprised heavy metal was needed to "balance"/unbalance a typical steel flywheel There's lots of places to drill.
The values you provided have me a bit confused.
Simple Unbalance results from a weight (mass, really) at a radius. For the 125.5/156.1 gram "unbalances" the radius of application should be known. If either weight was applied exactly on the crank centerline the radius would be zero, and unbalance would be zero, too.
23.44 oz-in ~ 665 g-in..........divide by 125.5 gram = 5.298 radius.
24.45 oz-in ~ 693 gr-in ........divide by 156.1 gram = 4.443 inch radius
In addition to weight and radius, angular position is important. early Chevy cranks and flywheels had a dowel to enforce a particular installation orientation. If your dowel is missing, it is possible to put the flywheel on 5 wrong ways and 1 correct way. Or, If the balance shop created the "right" unbalance in the "wrong" angular position, it could be real bad. Way more than a shivering rear view mirror. More like a circus ride at 3000 rpm and getting worse with revs.
Are the new drilled holes opposite the "heavy metal", making a REAl heavy spot on the flywheel? That heavy spot should be installed oriented inline with the back counterweight. Approximately inline with the front rod journal ( 1 and 2)