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The PBGC provides (if the distributee’s benefit is more than the ERISA § 203(e) amount [$5,000]) a joint-and-survivor annuity, unless the distributee elects, with the spouse’s consent, a different form of distribution. Pages 60812-60813, 60828-60829 https://www.govinfo.gov/content/pkg/FR-2017-12-22/pdf/2017-27515.pdf For the forms and instructions, https://www.pbgc.gov/prac/missing-participants-program.

Exactly - that's why it's there.

Would they be eligible to use the PBGC's missing participant program for DC plans? https://www.pbgc.gov/prac/missing-p-defined-contribution

Maybe I'm misunderstanding the question, but in DOL Advisory Opinion 2012-02A, the DOL said that making the matching contribution to another plan would cause the 403(b) plan to be an ERISA Title I plan.

Clarification: You MAY need to file a claim for benefits. The plan administrator may correct any improper reduction in your benefit informally based on having the mistake pointed out. Then it is the plan administrator's separate concern about the overpayment.

Why do you think you need recourse? First check with the plan administrator about your benefit. If it is not what it should be, then you need to file a claim for benefits. You should be able to do that without starting payment. If your benefit is improperly reduced because of the mistaken calculation of the AP benefit, then you will need to proceed through the claims procedures to get a correction. If your benefit was not adversely affected, overpayment to your ex is not your concern.

The answer to your question is yes. The 401(a) plan could be designed to be an ACP test safe harbor plan.

I am not a tax expert but my understanding is that 401(k) contributions are not included in salary reported on the corporate tax return (just as they are not included in Box 1 of the W-2). They are deducted as pension contributions. From the instructions to Form 1120S:

I think this should work. 26 CFR § 1.401(m)-1(a)(2)(ii) provides that The clear implication is that an employer contribution made to a defined contribution plan on account of contributions made by an employee in a plan that is intended to be a qualified plan or other arrangement described in § 1.402(g)-1(b) is a matching contribution, even if the plan to which the employer contribution is made is separate from the plan to which the employee deferral is made. In the context of governmental plans, it is common to have a 457(b) plan with matching contributions made to a 401(a) plan. Obviously, this doesn't work in the private sector, because a private sector 457(b) plan can cover only highly compensated employees. But it does reinforce the idea that matching contributions can be made to a plan other than the plan under which the employee made deferrals.