You are on the right track. Fraxel Repair CO2 is one of the most well-respected fractional "ablative" lasers on the market. Ablative lasers actually vaporize tiny columns of tissue so your scar area would be physically reduced by a small percentage. By feathering into the uninjured tissue area you would also likely see a lessening of the demarcation between the two areas ( injured and healthy).
Burn scars are typically more resistant to improvement than other injury scarring because burns cause more collateral damage than a cut. The underlying skin layers of burned areas are unevenly affected so that is one reason many burn scars look more "bunched".
I am puzzled that you have been told that Fraxel would make your scar worse. There are studies ongoing about the effectiveness of Fraxel Repair for burn and other scarring. Fraxel Restore requires multiple sessions and does not affect the skin at the same deep levels as does Fraxel Repair.
Although a single treatment may not provide sufficient improvement, two or three Fraxel Repair treatments most likely would give you enough tissue modification to satisfy you.
You don't mention the age of the scar. If still red, vascular laser would help (though do be careful that you choose a dermatologist or surgeon who has expertise around the eye area). If white or mixed color as most burn scars resolve to, then a fractional CO2 laser is a definite potential improvement vehicle.