I want to mount screw eyes in my hidden bondage rig. The wooden beams on either side are 7cm (ca 2¾ inch) thick. The screw eye's rod/ screw part is 12cm (ca 4¾ inch) long, of which 5.5cm (ca 2¼ inch) are threaded. The ring's outer ∅ is 3.5cm (ca 1½ inch). Image for reference.

Here's how I imagine it.

If I just screw in the threaded 5.5cm, the rest will protrude by about 9.5cm (ca 3½inch). Optimally, I'd like the ring to be as close to the wood as possible.

Which is the safest option? I don't want the wood to tear out under stress, and I can't have the screw come out the other side - it would be too visible.

If the steep angle is the best choice, how do I drill this reliably? I don't have a drill press or advanced tools, just a hand drill. The wooden beams are already mounted on the wall and it would be a major effort to remove them for drilling somewhere else.

Also, pics of the whole thing are soon to come!