How do I fix this handle?

[liveaboardL]

The screw broke off in the middle of the top-handle. The wedge broke off while unscrewing the screw, at the same time the screw broke in half.

My strategy so far, and I'm ignorant regarding this stuff is to:
1 try to drill into the center of the screw and drill it out starting w/ the smallest sized bit and moving up. The problem w/ this is centering the drill bit into the screw. The broken off screw is about 2" deep.

Once I get the screw out I can professional liquid nails the chipped wood together and try to insert a larger screw... No, if the top part is cracked like that there's not enough wood to put in a larger screw.

So I will have to just drill another hole next to the present hole and insert a new screw... No, I need 2 sized drill bits. The smallest one will go about 2.5" deep, to open the way for the new screw, and the larger one will go about .75" deep, to allow the screwhead to go all the way into the wood, and still have enough screw length to get a good hold of the top handle.

Now as for the top handle, you see it has a big crack in it. Is the best thing to do, to pry that crack off and pro liquid nails it together, or to try to use my finger to jam the PLN into the crack and then use a vice-grip pliers to hold it together for 3 days until it's fully cured?

Also, I don't have much room to drill into the aft-side of the handle-chunk, but there's plenty of room on the forward side. Putting a hole on the aft side of the current hole will make a better seal. I don't want this leaking when it rains. I plan on putting silicone around the new hole before I clamp it and also filling the current hole with silicone too.
I currently have pro liquid nails and silicone adhesive. A trip to the store takes about half a day for my rowboat, so, I'm going to try to use what I have. I have several different sized screws as well. Thanks for any input from your experience.

[Cap Erict3]

I use a centering bushing when drilling out bolts and screws. Use a rivet, nut, washer or what you have that will fit in the hole and center your bit.