I watched someone work on my COE that were hung up on the drum the same way. He used long spikes or punches and "walked" the drum off the shoes by prying, starting between the backing plate and the drum. It damages the shoe material but you will probably want new shoes or linings anyway. It took awhile as you gain a fraction of an inch each time. He worked his way around and around and eventually you could start to see the shoes and then the drum came off.
