Looks like you have a lot of old info. When I mean Posen city I will say so as opposed to Posen county (or Grand Duchy). Those naturalized would be born before 1810. My tree in [ ]
Alprsh: [I have Alperovich in my tree], b. Russia. No Alprsh in my book, closest Alport.
Apter: [none in my tree]; book closest Appel and Apt b. Kempen, Posen
Aryeh: No "Ary..."
Lichenstad: 1-- Herz Lichtenstad, living in Kempen, Posen (now Kepno, Poland), Kaufmann, naturalized 21/8/1834. Previously naturalized which means older and wealthier. I have Lichtenstein in my tree from Kempen.
Barnett: closest is Barnas in book, 2 both from Fordon, Posen.
Benas: 1 Lewin Benass in Krotoschin, a Kfm, u, Liferant, naturalized 22/9/34. Liferant is a distributor or contractor; Kfm is Kaufman or businessman.
Berliner: 2 Berlin, 9 Berliner. 4 from Ostrowo, 1 Kempen, 1 Posen city Simon a Schneider (tailor).
Casas: closest Caspar
Gunzberg: closest Grunberg
Haim: 2 Chaim [one in my tree from Posen settled in California]; closest Hahn, Solomon Heim from Plechin,
Loew: 2 Lowe; 1 Loewe, 7 Lowy (all have umlout on 'o' which means 'oe'.
Litchenstad: none but lots of Lichtenstein and 2-- Bar Lichtenstadt in Krotoschin a Vice-Rabbiner 22/9/34.--Herz Lichtenstadt in Kempen a Kaufmann 21/8/34, previously naturalized. Bar has unlout over the 'a' meaning 'ae'
Mirels: closest Mirls Heyman from Wreschen a Kaufmann 18/8/34.
Phillips: [lots in my tree one from Posen city]; closest in book Philipp 6.
Radenz: unsure of name
Sherach: closest is 8 Scherck (and one Scherk) which is my family, of which I have lots of info. Sherach sounds like the same as Schereck/Scherek/Shirek etc. Now if Charlotte Sherach might be the elusive Mrs Constance Shirek I have been looking for for 10 years, that would be great. Can you tell me more about her please, all you know if you will. mine was born jul 1851 Posen city and died 1928 San Francisco, CA. Where can i find "Neil Rosenstein's The Unbroen Chain"?