hallel as a reading of pesukim

In order to escape the dilemma of wanting to recite hallel to commemorate Yom ha’Atzmaut and/or Yom Yerushalayim but wanting to avoid the problem of there not being a takanah which would license it, some add the hallel without a bracha only at the conclusion davening after the last kaddish.  This way, the recitation of hallel is not formally part of tefillah, but counts only as reading pesukim.  If someone wants to say tehillim and just happens to read the perakim that we recite for hallel, there is no need for a takanah and no problem in doing so.

One thing that bothers me about this solution is that if one is just reading pesukim, then one would not add “hodu” responsively after “yomaru na …” and “yomar na…”  and one would not double pesukim like we do in the section before/after “ana Hashem…”   These are features particular to kri’as hallel (see Sukkah 38b).  From what I have seen done, no one changes how the hallel is read -- I'm not sure why.