Some stabilizing solutions can soak the wood for an extended period of time without a vacuum chamber. I have one, so I can not say how well penetration will work on horn without the use of a vacuum. I can say, it usually takes several hours before the bubbles stop. Typically we leave them overnight just to be sure. When they come out, they dry a little on a rack we made with a 2x4 scrap and some dowels (actually I think the original used disposable chopsticks from takeout) Once the BLO dries on the surface, we continue turning the blanks.
Keep in mind, I'm absolutely no expert in stabilization. I will say, I just pulled out a roll of buffalo horn pens that were intended for a wholesale bulk buy that never paid. After several months of being moved from room to room, building to building and eventually tucked on a shelf in the garage, these are not showing one sign of cracking or issue. We also have not seen one pen come back since we started this process over a year ago. Before that, a few would come back here and there.
If you have success with any other methods or ideas, please pass them along.
Happy Turning!