LED bulbs won't screw in far enough
Don't do this -- it'll expose some of the threads on the bulb, which are connected to the neutral.  (It's a good way to get bit if you need to change the bulb again.)

An E26 to E26 extender should fix this without causing any safety issues.  You can also try turning the power off at the breaker and bending the back (hot) contact of the bulb base up with a wooden tongue depressor or other suitably nonconductive instrument so that it makes contact with the hot contact on the bulb.