401k termination/403b in controlled group

Sponsor maintains 401k and 403b.  All employees in controlled group are employed by nonprofits.  Sponsor wants to terminate 401k and force nonresponsive participants to direct rollover to 403b.  Or alternatively to force direct rollover to safe harbor IRA.  Is force out available at all here?  1.411(a)-11(e) says no force out if another defined contribution plan in controlled group other than ESOP.  Is 403b plan considered another defined contribution plan for this purpose?  414 definition suggests yes?  It seems like a catch 22 - can’t force to IRA and can’t transfer to 403b as that isn’t allowed.  Maybe the 403b is not a defined contribution plan and so we can force out to an IRA?  But I can find no path  or support to forcing a direct rollover to the 403b.  Maybe a “transfer” where 411d6 is honored, but again - can’t transfer 401k to 403b.  Help…

Treas. Reg. § 1.401(k)-1(d)(4)(i) provides:

(4) Rules applicable to distributions upon plan termination—(i) No alternative defined contribution plan. A distribution may not be made under paragraph (d)(1)(iii) of this section if the employer establishes or maintains an alternative defined contribution plan. For purposes of the preceding sentence, the definition of the term “employer” contained in § 1.401(k)-6 is applied as of the date of plan termination, and a plan is an alternative defined contribution plan only if it is a defined contribution plan that exists at any time during the period beginning on the date of plan termination and ending 12 months after distribution of all assets from the terminated plan. However, if at all times during the 24-month period beginning 12 months before the date of plan termination, fewer than 2% of the employees who were eligible under the defined contribution plan that includes the cash or deferred arrangement as of the date of plan termination are eligible under the other defined contribution plan, the other plan is not an alternative defined contribution plan. In addition, a defined contribution plan is not treated as an alternative defined contribution plan if it is an employee stock ownership plan as defined in section 4975(e)(7) or 409(a), a simplified employee pension as defined in section 408(k), a SIMPLE IRA plan as defined in section 408(p), a plan or contract that satisfies the requirements of section 403(b), or a plan that is described in section 457(b) or (f).