Is the traditional "Blessing of the Children" allowed?

Question

There is a traditional blessing a parent/father says for his children in many communities on returning from the synagogue on the nights of the high holy days or all Friday nights, etc. The text published in most siddurim comprises a fragment of a verse in Genesis (48:20) as well as the verses of the blessings of the priests (Numbers 6:24-26).

Halachic issues that seem to arise with this formulation are 1. the problem with reciting verse fragments (כל פסוקא דלא פסקיה משה אנן לא פסקינן ליה - "Any verse-break not according to the verse-breakup-up of Moses..."; see e.g. Tractate Megillah 22a) as well as 2. the apparent biblical prohibition of a non-priest using the priestly blessing (see e.g. Rama Orach Chaim 128:1).

Do any authorities specifically address these issues with regard to this tradition? Are there any alternate formulations traditionally used?

Related:

Blessing the Children on Friday Night

Should a parent bless a child resting one hand or both?

Answer 1

Just came across Halachipedia's bit on this (which perhaps is more of an ex post facto limud zechus on an established custom rather than an a priori, l'chatchila leniency):

...parents blessing their children and Rabbis blessing their students, may put both of their hands on their heads while reciting the blessing, since the only prohibition is to make the blessing with the intention of fulfilling the mitzvah of the commandment, and to do it like the cohen.

Yalkut Yosef, Tefillah Volume 1, page 296. See Beiur Halacha 128:1 s.v. DeZar who writes that the minhag of Yisraelim to bless other Jews with the words of Birkat cohanim is either based on the fact that perhaps there's only a prohibition if they raise their hands like cohanim or that they have kavana not to fulfill the mitzvah of Birkat cohanim.