Second on the double sided tape, but let’s back up a little bit. You say you want to do a good job and don’t want your forstner bit to wander. Don’t half-[censored] the job. Undo the fasteners in the two bed boards and do the job the previous guy didn’t want to. It won’t take that much time, and you won’t have a 1 1/4” forstner chowdering your finished planks because you didn’t get good contact with your guide plank because you reused the double sided tape instead of replacing it for each new hole.
Line up the hole you want to drill and then clamp the board down to your drill press, or clamp your drill guide to your bed board so it won’t move. Then, drill comfortably knowing (not hoping) your bit isn’t going to wander.
