I don't know why the company would indicate that there is no option to deposit the money into an employee's spouse's HSA (assuming that is willing to make the contribution under these circumstances at all) unless the employer simply has not implemented a procedure to do so. It is perfectly acceptable under the law, is not particularly uncommon and TurboTax has specific provisions reporting a code W amount on one spouse's W-2 as having been deposited into the other spouse's HSA.
HSA contributions on behalf of an eligible individual, your spouse in this case, can be made by anyone. If the employer will make an HSA contribution, but only to your HSA despite you being ineligible, let them make the contribution, obtain a return of excess contribution, then make an HSA contribution on behalf of your spouse to your spouse's HSA. The result will be the same as if the employer had made the deposit to your spouse's HSA (except for the taxation of any gain required to be distributed with the return of excess contribution). In this case you would tell TurboTax when entering your W-2 that the entire amount was deposited into your HSA, that you obtained a return of excess contribution of this amount, and that you made a personal contribution of this amount to your spouse's HSA. The result would be that the excess amount would not be included in income on your Form 8889, would be included (along with any attributable gains) in income on line 21 of Schedule 1, would be included as a personal HSA contribution on your spouse's Form 8889 and would appear as a deduction on line 25 of Schedule 1 (essentially offsetting the amount on line 21).
