The Brummbar was mainly used by Sturmpanzerabteilung 216, 217, 218 and 219.
216 moved to the Eastern front in June 1943 and fought at Kursk. It was then refitted in Sept and fought in Russia until Dec, where it moved back to Germany. It moved to Italy in Feb 1944 and fought there until the end of the war.
217 formed between Apr - June 1944 and was sent to Normandy in July where part of it was destroyed at Falaise, while the rest return to Holland. It took part in the Ardennes offensive, and then fought defensively while retreating, ending up the war in the Rhur pocket in April 1945.
218 began forming in Jan 1945 and was ready for combat in March.
219 was formed in Sept 1944. In Dec, it was moved to Hungary. In Jan 1945, it took part in the fighting around Budapest as part of 23rd Panzer Division. In March, it was moved to Czechoslovakia to be refitted after losing all their Brummbars.
An independant company was formed in Aug 1944, called Sturmpanzer-Kompanie z.b.V. 218. It took part in the fighting around Warsaw during the uprising. It stayed in Poland until becoming part of Sturmpanzerabteilung 218 in Jan 1945.
This is what I could find on Achtung Panzer, and could not find anything else saying something different in my other references. Sturmpanzer-Kompanie z.b.V. 218 and Sturmpanzerabteilung 219 would be your best choices for an late Eastern front setting.