Can I have a non-compete waived or released?

I was recruited by a competitor for a job that will consist of (exec) managing billing and collections. I will have no sales or marketing contacts and will manage tasks that in my opinion will pose no threat to my former employer.

I disclosed my non compete to the new employer, I expected the job to start around the time my year would be over. Therefore, no issue. I was offered the job at a generous salary and as soon as I asked to level-set about the non compete as the start date was sooner, I was basically told I was unhired and the recruiter overlooked the noncompete that was listed on my app - as well. Can I ask for a waiver, as I have been away from the employer for 6 mos and if start dte is sooner, would be only 3 months left on my non-compete. How to do this successfully? I asked if my start date could be pushed back and was told "absolutely not". I think the recruiter wants to sweep this error under the rug. I am told that the new employer's legal counsel will review, but I will probably not be hired now. This is so upsetting as I pose no threat by running a billing department. Can someone help?