Originally, Minhag Ashkenaz was to recite selichot, accompanied by the 13 middot, during chazarat hashatz of all prayers of Yom Kippur. For various reasons, the vast majority of congregations today omit them in shacharit, musaf and mincha, and most of the commonly-printed machzorim print no selichot in these prayers. (See e.g. here for further discussion.) These selichot are recited after ya'aleh veyavo, and are followed by zechor rachamecha (which is printed in machzorim).
Consider a synagogue that wishes to recite the 13 middot, but does not want to publish separate booklets / handouts of selichot to be recited. One possible solution would be to recite the 13 middot in conjuction with (either during or immediately following) the 'chatanu' selichot, which are said after zechor rachamecha and before zechor lanu berit avot and which do appear in the machzorim. This has the advantage of allowing congregants to use only their machzor, without needing a separate source for additional piyutim.
Are there any sources discussing the legitimacy / advisability of such a practice? I note that classically, the 13 middot would only be recited before zechor rachamecha, but is there any problem doing so afterwards?
