your timeline is off. In the thousand years between the churban and the rishonim were the tanaim, amoraim, rabonon savorai, and geonim.
+1
using approximate secular years
70 - churban
450-500 - chasimas hatalmud
600 - Geonim start.
mohammed died in 632, so this is also the tekufa of the Muslim beginning, caliphates etc. Bustenai, wasn't particularly restful I think
740 was the Khazar Hingdom, which lasted 500 years. might be the answer to OP's quest
this tekufa also had the Kairaites etc. made a lot of trouble as well
942 - Reish gelusa was abolished, but had lasted 700 years
Rashi was born in 1040