I will recommend that you allow your attorney to work with the employer to resolve the contract dispute. Your efforts to do so may only make your counsel's job that much more difficult.
I agree with my colleague, and you should hire a lawyer to negoiate for you so your employer will take this threat of a lawsuit seriously, perhaps on a sliding scale to incentivise them to handle it quickly. If you do this yourself, you could make damaging admissions.
The strength of your claim depends on the strength of your contract. If it doesn't provide for legal fees to the prevailing party, then you won't be able to add the money you spend on a lawyer to your claim, and be made whole. Realize, also, that settlements often involve the claimant taking less than they want and the recipients paying more than they want -that's a true settlement, and no one's happy with it, but it does end the matter.
PLEASE READ THIS BEFORE YOU COMMENT, EMAIL ME OR PHONE ME. I'm only licensed in CA. This answer doesn't make me your lawyer, and neither do follow-up comments and/or emails and/or phone calls, and you shouldn't expect me to respond to your further questions if you haven't hired me. We need an actual agreement confirmed in writing before any attorney-client relationship is formed. This answer doesn't constitute legal advice, and shouldn't be relied on, since each state has different laws, each situation is fact specific, and it is impossible to evaluate a legal problem without a comprehensive consultation and review of all the facts and documents at issue.