As you correctly pointed out, this is the boat you find yourself in when you attempt to change the history level of an already running deployment (similar to what you’ll find in this post).
I think all you need to do is change the historyLevel entry in ACT_GE_PROPERTY to be the id of your custom history level implementation. Per the docs found here, your implementation should have an implementation for getId. Use this value. That way the single entry in the database (id) matches the single entry of <property name="history">custom-variable</property> in your config.