> that would be two holes at the top on opposite sides, right?

If you mean opposite sides of the void, yes. Wouldn't have to be opposite sides of the wood. As mark noted, venting at the top would be best. It's like trying to drink out of a soda bottle. You've got to let air in to get the soda out. Otherwise you only get a little, and then get your lips sucked into the bottle. Same in reverse, and with filling a void.

> I did that once, I'll do it again on the one that drill through, since the
> structural integrity is obviously compromised.

Are you saying structural integrety was compromised by the drill hole? If so, I think you're over doing it with the concern. The void itself is far more significant.