I've done a bit of looking into pre-1914 Austro-Hungarian ministers, and come up with the following list. The start date of a few existing ministers should also be changed - Berchtold and Bilinski to 1912, Conrad to 1906, and Haus to 1913. Also, I don't have any suggestions as of yet for traits.
Head of Government
1897 Kasimir Felix von Badeni (A) / Dezső Bánffy (H)
1897 Paul Gautsch von Frankenthurn (A) / Dezső Bánffy (H)
1898 Franz von Thun und Hohenstein (A) / Dezső Bánffy (H)
1899 Manfred von Clary und Aldringen (A) / Kálmán Széll (H)
1899 Heinrich von Wittek (A) / Kálmán Széll (H)
1900 Ernst von Koerber (A) / Kálmán Széll (H)
1903 Ernst von Koerber (A) / Károly Khuen-Héderváry (H)
1903 Ernst von Koerber (A) / István Tisza (H)
1904 Paul Gautsch von Frankenthurn (A) / István Tisza (H)
1905 Paul Gautsch von Frankenthurn (A) / Géza Fejérváry (H)
1906 Konrad zu Hohenlohe-Waldenburg-Schillingfürst (A) / Sándor Wekerle (H)
1906 Max Wladimir von Beck (A) / Sándor Wekerle (H)
1908 Richard von Biernerth-Schmerling (A) / Sándor Wekerle (H)
1910 Richard von Biernerth-Schmerling (A) / Károly Khuen-Héderváry (H)
1911 Paul Gautsch von Frankenthurn (A) / Károly Khuen-Héderváry (H)
1911 Karl von Stürgkh (A) / Károly Khuen-Héderváry (H)
1912 Karl von Stürgkh (A) / László Lukács (H)
Foreign Minister
1895 Agenor Goluchowski (Died 1921)
1906 Alois Lexa von Aehrenthal (Died 1912)
Armaments Minister
1882 Benjamin Kállay
1903 István Burián von Rajecz
Chief of Staff
1881 Friedrich Beck-Rzikowski
Chief of the Army
1881 Friedrich Beck-Rzikowski
Chief of the Navy
1897 Hermann von Spaun
1904 Rudolf Montecuccoli
Head of Government
1897 Kasimir Felix von Badeni (A) / Dezső Bánffy (H)
1897 Paul Gautsch von Frankenthurn (A) / Dezső Bánffy (H)
1898 Franz von Thun und Hohenstein (A) / Dezső Bánffy (H)
1899 Manfred von Clary und Aldringen (A) / Kálmán Széll (H)
1899 Heinrich von Wittek (A) / Kálmán Széll (H)
1900 Ernst von Koerber (A) / Kálmán Széll (H)
1903 Ernst von Koerber (A) / Károly Khuen-Héderváry (H)
1903 Ernst von Koerber (A) / István Tisza (H)
1904 Paul Gautsch von Frankenthurn (A) / István Tisza (H)
1905 Paul Gautsch von Frankenthurn (A) / Géza Fejérváry (H)
1906 Konrad zu Hohenlohe-Waldenburg-Schillingfürst (A) / Sándor Wekerle (H)
1906 Max Wladimir von Beck (A) / Sándor Wekerle (H)
1908 Richard von Biernerth-Schmerling (A) / Sándor Wekerle (H)
1910 Richard von Biernerth-Schmerling (A) / Károly Khuen-Héderváry (H)
1911 Paul Gautsch von Frankenthurn (A) / Károly Khuen-Héderváry (H)
1911 Karl von Stürgkh (A) / Károly Khuen-Héderváry (H)
1912 Karl von Stürgkh (A) / László Lukács (H)
Foreign Minister
1895 Agenor Goluchowski (Died 1921)
1906 Alois Lexa von Aehrenthal (Died 1912)
Armaments Minister
1882 Benjamin Kállay
1903 István Burián von Rajecz
Chief of Staff
1881 Friedrich Beck-Rzikowski
Chief of the Army
1881 Friedrich Beck-Rzikowski
Chief of the Navy
1897 Hermann von Spaun
1904 Rudolf Montecuccoli