Another variant, instead of making the Withdrawer immune to the Immobilizer, you may specify that you want to capture the Immobilizer with an immobilized piece, and the Immobilizer's owner specifies how this will be done, and in this case only the immobilization is ignored. You said Immobilizer seem too powerful, this is another way to make it weak, and in some cases may add some additional complications to the strategy (especially if there are multiple captures possible in this way).
Another variant, instead of making the Withdrawer immune to the Immobilizer, you may specify that you want to capture the Immobilizer with an immobilized piece, and the Immobilizer's owner specifies how this will be done, and in this case only the immobilization is ignored. You said Immobilizer seem too powerful, this is another way to make it weak, and in some cases may add some additional complications to the strategy (especially if there are multiple captures possible in this way).