Agree, if you were saying both, I’d think it would go before. 2 separate reasons to be Makdim Tachanun to Hsllel:-
1) Perek 6 in Tehillim precedes Perek 113-118, and if read in Serugin {wrong order} probably not Yotzei.
2) Todir veShe’Eino Todir:- Todir Kodem.