I don’t know any reincarnation mangas that are completed so uh this reddit post https://www.reddit.com/r/Isekai/comments/91desw/recommend_me_a_finished_manga_about/
I totally feel you cause I'm a big fan of isekai but they're never finished and it usually takes ages to update. Unfortunately, there aren't many isekai mangas that are completed, at least not from what I know.
For similar settings to what you're looking for (noble settings, non-modern world, etc.), I recommend these (although they are not isekais):
http://www.mangago.zone/read-manga/empress_of_another_world/ (girl from another world)
http://www.mangago.zone/read-manga/light_shadow/
NOTE: Both of these are completed.
Another recommendation is:
http://www.mangago.zone/read-manga/cheating_men_must_die/ (involves similar setting to isekai and past life memories but is less shoujo and more taking revenge on men in novel-like worlds on behalf of the original owners of the body)
NOTE: this is unfortunately not completed yet but has over a 100 chapters and is a pretty good read as there are arcs.
These are my recs though I'm not sure if you have read them yet but hope you enjoy ヾ(❀╹◡╹)ﾉ~
I have another rec if you haven't read it, not isekai but she has past memories and lives (reincarnation) plus it's completed: http://www.mangago.zone/read-manga/this_time_i_will_definitely_be_happy/
Every single isekai where someone dies and goes into a noble family setting and has past life memories and shoujo overflow
is in ongoing and i cant bearrrrrrrrr the wait anymore. any loooong completed ones like this.