https://www.irs.gov/businesses/small-businesses-self-employed/sale-of-residence-real-estate-tax-tips....

Maybe IRS really doesn't care if it is reported:

Reporting the sale

Report the sale or exchange of your main home on Form 8949, Sale and Other Dispositions of Capital Assets, if:

• You have a gain and do not qualify to exclude all of it,
• You have a gain and choose not to exclude it, or
• You received a Form 1099-S.

If it were me, I would report it anyway. You have already spent this much time, get it right and bill the client. The next time will be much easier