I think that’s what 619Diofan was talking about, as well as what was in Eric’s video. As long as you are careful, you should be able to drift it out from the other side.
How big is the slide hammer you are using? The reason I ask, I saw one that a friend bought from HF, the thing is like maybe 2 pounds and probably can’t pull a spoon out of peanut butter. You probably need one of the 5 pounders on this job.