Overwithheld NJ State Tax first half of 2022

Hi All-

 

My employer withheld NJ taxes at an extremely high amount throughout the first half of the year ( their error) , It was corrected in July to a normal monthly rate. The amount withheld was so high that i am already way past my liability paid with 5 months to go. Other than claiming the max allowances is it pretty much a situation where i just need to wait till i file to get a refund? Would claiming EXEMPT for 5 months be considered illegal ( reading through the NJ exempt form it seems it would be illegal)? My employer insists since they already paid it theres nothing more they can do.