My reading of that IRS page is that the plan must treat itself as terminated for purposes of vesting, but not that the IRS will treat it as terminated or force it to terminate. The compliance unit identified plans that discontinued contributions and all they did was make them 100% vest, with no mention of forcing them to terminate and without any clear reference to special reporting or a dedicated Form. It said some of them had to amend their 5500s, but with regard to vested participants, not to report as a discontinued plan and not to mark a 5500 as final.
So I read that as evidence suggesting the IRS does not, as a practical matter, require termination or even require extra reporting for plans that discontinue contributions.
Whereas this page makes it sound more ironclad that the IRS does not treat a plan as fully terminated until the termination date is set, the benefits/liabilities are determined, and the assets are gone.
Though for the original question, I think it will probably make sense to just terminate.