I stand (partially) corrected.  When I first started doing taxes, the Form 8919 did not option H

"I received a Form W-2 and a Form 1099-MISC and/or 1099-NEC from this firm for 20XX.  The amount on Form 1099-MISC and/or 1099-NEC should have been included as wages on Form W-2. (Don't file Form SS-8 if you select reason code H.)

But does anyone know what will happen to the employer if 8919 is filed with code H?  Is it the same as when the SS-8 is filed (that the IRS is going to go after the firm anyways). 

If so, then I would still explain to your client what you are doing and the repercussion (that they may lose their job because they reported it correctly).  So, I would still have that discussion with the clients whether to ask for a corrected W2, or report on 8919.

But as the instructions you found pointed out, you cannot report it as "other income".  At least half of the self-employment taxes must be paid when the tax return is filed.