This is our fix:
We started by placing three sets of shims under each dresser making the front a bit higher than the back. This helped the dresser to tip less easily but with these dressers securing to the wall was absolutely necessary.
We tried to secure the L-bracket to wall studs where we could. We used two L-brackets per dresser. A bracket on each dresser was secured to a stud & the other through the dry wall with a Walldog screw. We drilled holes first for all the screw placement including the top of the dressers. If these were heirloom dressers, we would have found a less obvious place to place the L-bracket on the dresser, but these are not & right now it’s all about safety.
We tested the brackets by opening all the drawers to see if more work was needed. The dressers held in place well!