I can only suggest you play around the various options on the TFL Journey Planner, and see what that offers up. Tweak walking speed etc, see the options.

I'm not sure there's any amazingly quick option though, given the closure of the fast lines, but you might find something that works fairly well. Especially if you put in the real destination, there might be a short cut for going where you really want to be, not just the station.

Also, it's perhaps worth checking again in a few months. There may be a rail replacement bus that hasn't been loaded into the system yet