tefilla - Neilah tefillah shabbas nusach of בו

On a regular shabbas the teffilah of retzei vhachlitzainu in shmoneh esri has three variations:

1. 
   

   In maariv it is בה .

   
   


2. 
   

   In shachris and musaf it is בו.

   
   
   


3. 
   

   In mincha it is בם.

   
   

There is a reason for this difference (gematria or a parable of a bride).

My question is, when Yom Kippur falls on shabbas, my machzor uses בו in neilah. Is there a reason for this (other than the editors forgot to differentiate)? Shouldn't it say בם since it is after mincha?