I just want to second the point that some others have made that it seems more accurate to say only that Harsanyi's result supports utilitarianism (rather than total utilitarianism). Adding the word "total" suggests that the result rules out other version of utilitarianism (e.g. average, critical-level and critical-range utilitarianism), which as you point out is not correct. More generally, I think "utilitarianism" (without the "total") nicely signals that Harsanyi's result concerns fixed-population settings.
It is also worth noting that Harsanyi himself accepted average utilitarianism rather than total utilitarianism in variable-population settings (see the letter exchange between him and Yew-Kwang Ng reported in the appendix of Ng, Y. K. (1983). Some broader issues of social choice. In Contributions to Economic Analysis (Vol. 145, pp. 151-173). Elsevier.).
Anyway, thanks for this post!
[Edited comment to remove grammatical error]