How do I force a tight globe-valve water shutoff to fully close?
Any valve that refuses to fully shut off won't be improved by tightening the handle further. 

The usual problem with a Globe Valve is that the rubber valve seal has aged and cracked, needing replacement. This means you have to shut the water off upstream of the valve and remove the body cartridge so the rubber seal can be changed out.



Some valves have a globe shape, but get misidentified by that shape because they actually are Gate Valves which have a vertical wedge shaped metal gate that gets pushed down into a tapered slot. These fail because sediment accumulates in the slot on the downwards side and the gate no longer can be pushed fully home so the taper seals. This requires the water to be turned off upstream so you can take the top off the valve, extract the gate and grub the sediment out using a piece of welding rod so it will flush out when you reassemble the valve.

I've gone over to using quarter turn ball valves when I have to go to this much trouble. They are better than Globe Valves because the opening is the same size as the inner diameter of the pipe when the valve is full open, the water doesn't have to turn 90 degrees to flow through a restriction as it does in a Globe valve and while the gate valve has the same lack of restriction as the ball, the ball valve has no slot for rust, sand and sediment to accumulate in while it spends most its life wide open.