Hi, Johnno
There were two separate expeditions involving the Canadian Army into the Russian Civil War (plus several individual Canadians, such as Raymond Collishaw of the RAF, who ended up serving in various other intervention forces). As you've noted, the Canadian Army contributed an artillery battery that saw action near Archangelsk in November 1918 alongside British and American forces in support of the Whites and against the 'bolos' (or Reds). The CSEF was a separate expedition which saw Canada contribute a brigade-sized force to Vladivostok.
The CSEF really just hung out in Vladivostok and saw no significant action in Russia. There was pressure from British Army leadership to dispatch the CSEF up the Trans-Siberian Railway to Omsk to support Kolchak's White forces, but the last thing Canadian Government wanted was to get dragged into the RCW at the time that everyone else was doing their damnedest to get out. As a result, the Canucks mostly hung around Vladivostok then eventually shipped back to Victoria so they could be discharged to peacetime life.
As a fun counterfactual you could send your Canucks to reinforce Kolchak's army, but if you want to recreate an actual conflict, you should look at the Battle of Tulgas in North Russia in November 1918, but you'd need the troops in winter kit, probably the best bet being the Tiger Miniatures troops that Argsilverson mentions. You'd also need Brits, Yanks, Whites and Reds to complete the game, and possibly river gunboat...