I wish I had seen your post earlier. Hammer a piece of rebar (metal stake) up against the trunk (long enough to run up the trunks side) and hammer into the ground. This will not harm any yucca roots it may touch or disturb. Then take a bungee tie stray and wrap the trunk up against the rebar stake.
This will effectively stabilize the trunk from wind or top heaviness of the branches. Its always worked for me without fail.